SAT Equivalent Expressions Practice Questions | Download PDF

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The SAT equivalent expression practice questions assess your ability to factor, extend, combine like terms, simplify rational expressions, or use exponent rules to rewrite an algebraic expression in a different but mathematically same form. There are 60 SAT-style equivalent expression questions on this page, with full solutions, answer options, and trap notes. The set progresses from simple simplification to more complex multi-step equivalency problems, factoring, exponent and radical rewrites, and manipulation of rational expressions..

In This Guide – 60 Equivalent Expressions Practice Questions

1. What does the SAT test in equivalent expressions?
2. How do SAT questions test basic simplification?
3. How do you handle factoring for equivalence?
4. How are exponent and radical rules tested?
5. How do you simplify rational expressions?
6. What do hard equivalence questions look like?
7. What mistakes cost students points?
8. How should you study equivalent expressions in 2 weeks?
9. Frequently asked questions

Start With SAT Math Topic-Wise Practice

Practice equivalent expressions with topic-wise SAT Math questions, full mock review, and targeted algebra correction.

SAT strategy: Enter a straightforward but non-trivial number (such as 2 or -1, avoiding 0 and 1) for the variable in both the original statement and each solution option if the algebra appears clumsy. Whichever option matches is probably the same.

Which expression is equivalent to 3(x + 4) − 2x?

A) x + 12    B) x + 4    C) 5x + 12    D) x + 6

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3(x + 4) = 3x + 12. Then 3x + 12 − 2x = x + 12. Answer: A

Which expression is equivalent to -2(x − 5) + 3x?

A) x + 10    B) 5x − 10    C) x − 10    D) -x + 10

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-2(x − 5) = -2x + 10. Then -2x + 10 + 3x = x + 10. Answer: A

Which expression is equivalent to 4(2x − 1) − 3(x + 2)?

A) 5x − 10    B) 5x + 10    C) 11x − 10    D) 5x − 2

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4(2x − 1) = 8x − 4; -3(x + 2) = -3x − 6. Combine: 8x − 4 − 3x − 6 = 5x − 10. Answer: A

Which expression is equivalent to 5x − (2x − 7)?

A) 3x + 7    B) 3x − 7    C) 7x + 7    D) 3x

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Distribute the negative: 5x − 2x + 7 = 3x + 7. Answer: A

Which expression is equivalent to 2(3x − 4) + 5(x + 1)?

A) 11x − 3    B) 11x + 3    C) 8x − 3    D) 11x − 9

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6x − 8 + 5x + 5 = 11x − 3. Answer: A

Which expression is equivalent to 6x² + 3x − 2x² + x?

A) 4x² + 4x    B) 4x² + 3x    C) 8x² + 4x    D) 4x² − 2x

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Combine like terms: (6x² − 2x²) + (3x + x) = 4x² + 4x. Answer: A

Which expression is equivalent to -(4x − 3) + 2(x − 1)?

A) -2x + 1    B) -2x + 5    C) 6x + 1    D) -2x − 1

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-4x + 3 + 2x − 2 = -2x + 1. Answer: A

Which expression is equivalent to (x + 3) + (x − 3)?

A) 2x    B) 2x + 6    C) x² − 9    D) 0

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The +3 and -3 cancel, leaving 2x. Answer: A

Which expression is equivalent to 3x(x − 2) + 4x?

A) 3x² − 2x    B) 3x² + 2x    C) 3x² − 6x + 4x    D) 3x² + 6x

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3x(x − 2) = 3x² − 6x. Add 4x: 3x² − 6x + 4x = 3x² − 2x. Answer: A

Which expression is equivalent to 7 − 2(x − 3)?

A) -2x + 13    B) -2x + 1    C) 2x + 13    D) -2x + 4

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-2(x − 3) = -2x + 6. Then 7 − 2x + 6 = -2x + 13. Answer: A

Which expression is equivalent to (2x − 1)(3) − (x + 4)?

A) 5x − 7    B) 5x + 7    C) 7x − 7    D) 5x − 1

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6x − 3 − x − 4 = 5x − 7. Answer: A

Which expression is equivalent to 2[3(x − 1) − 2x] + 5?

A) 2x + 1    B) 2x − 1    C) 8x − 1    D) 2x + 3

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Inside brackets: 3x − 3 − 2x = x − 3. Then 2(x − 3) + 5 = 2x − 6 + 5 = 2x − 1. Answer: B

Which expression is equivalent to (x + 2)² − x²?

A) 4x + 4    B) 4x + 2    C) 2x + 4    D) x² + 4

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(x + 2)² = x² + 4x + 4. Subtract x²: 4x + 4. Answer: A

Which expression is equivalent to 3(x − y) − 2(y − x)?

A) 5x − 5y    B) x − y    C) 5x + 5y    D) x − 5y

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3x − 3y − 2y + 2x = 5x − 5y. Answer: A

Download More SAT Math Topic-Wise Practice Questions

Use more topic-wise practice to strengthen factoring, rational expressions, exponents, and coefficient matching.

Which expression is equivalent to 6x² + 9x?

A) 3x(2x + 3)    B) 3x(2x + 9)    C) 6x(x + 9)    D) 3(2x² + 3x)

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The GCF of 6x² and 9x is 3x: 3x(2x + 3). Answer: A

Which expression is equivalent to x² − 9?

A) (x − 3)(x + 3)    B) (x − 9)(x + 1)    C) (x − 3)²    D) (x + 3)²

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This is a difference of squares: x² − 9 = (x − 3)(x + 3). Answer: A

Which expression is equivalent to x² + 7x + 12?

A) (x + 3)(x + 4)    B) (x + 2)(x + 6)    C) (x + 1)(x + 12)    D) (x + 3)(x + 5)

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Two numbers that multiply to 12 and add to 7 are 3 and 4: (x + 3)(x + 4). Answer: A

Which expression is equivalent to x² − 5x − 14?

A) (x − 7)(x + 2)    B) (x + 7)(x − 2)    C) (x − 14)(x + 1)    D) (x − 7)(x − 2)

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Two numbers that multiply to -14 and add to -5 are -7 and 2: (x − 7)(x + 2). Answer: A

Which expression is equivalent to 2x² + 5x − 3?

A) (2x − 1)(x + 3)    B) (2x + 1)(x − 3)    C) (2x − 3)(x + 1)    D) (2x + 3)(x − 1)

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Testing (2x − 1)(x + 3) = 2x² + 6x − x − 3 = 2x² + 5x − 3. Answer: A

Which expression is equivalent to x² + 10x + 25?

A) (x + 5)²    B) (x + 25)²    C) (x + 5)(x − 5)    D) (x + 10)(x + 5)

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This is a perfect square trinomial: (x + 5)² = x² + 10x + 25. Answer: A

Which expression is equivalent to 4x² − 16?

A) 4(x − 2)(x + 2)    B) 4(x − 4)(x + 4)    C) (2x − 4)(2x + 4)    D) 4(x² − 16)

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Factor out 4 first: 4(x² − 4) = 4(x − 2)(x + 2). Answer: A

Which expression is equivalent to 3x² − 12x + 12?

A) 3(x − 2)²    B) 3(x − 4)(x − 3)    C) 3(x − 2)(x + 2)    D) (3x − 6)²

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Factor out 3: 3(x² − 4x + 4) = 3(x − 2)². Answer: A

Which expression is equivalent to x³ − x?

A) x(x − 1)(x + 1)    B) x(x² − 1)    C) (x − 1)(x² + 1)    D) x(x + 1)²

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Factor out x: x(x² − 1), then factor the difference of squares: x(x − 1)(x + 1). Answer: A

Which expression is equivalent to 6x² − 5x − 6?

A) (2x − 3)(3x + 2)    B) (2x + 3)(3x − 2)    C) (3x − 3)(2x + 2)    D) (6x + 2)(x − 3)

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Testing (2x − 3)(3x + 2) = 6x² + 4x − 9x − 6 = 6x² − 5x − 6. Answer: A

Which expression is equivalent to xy + 3x + 2y + 6?

A) (x + 2)(y + 3)    B) (x + 3)(y + 2)    C) (x + 2)(y + 2)    D) (x + 6)(y + 1)

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Group: x(y + 3) + 2(y + 3) = (x + 2)(y + 3). Answer: A

Which expression is equivalent to x² − 1?

A) (x − 1)(x + 1)    B) (x − 1)²    C) (x + 1)²    D) x(x − 1)

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Difference of squares: x² − 1 = (x − 1)(x + 1). Answer: A

Which expression is equivalent to x² − 6x + 9 − y²?

A) (x − 3 − y)(x − 3 + y)    B) (x − y − 3)²    C) (x − 3)² − y    D) (x + y − 3)(x − y + 3)

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x² − 6x + 9 = (x − 3)², so the expression is (x − 3)² − y², a difference of squares: (x − 3 − y)(x − 3 + y). Answer: A

Which expression is equivalent to 9x² − 25?

A) (3x − 5)(3x + 5)    B) (9x − 5)(x + 5)    C) (3x − 25)(3x + 1)    D) (3x − 5)²

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9x² = (3x)² and 25 = 5², so this is a difference of squares: (3x − 5)(3x + 5). Answer: A

Which expression is equivalent to x³ · x⁵?

A) x⁸    B) x¹⁵    C) x²    D) 2x⁸

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When multiplying same bases, add exponents: x³⁺⁵ = x⁸. Answer: A

Which expression is equivalent to x¹⁰ / x⁴?

A) x⁶    B) x¹⁴    C) x²·⁵    D) x⁴⁰

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When dividing same bases, subtract exponents: x¹⁰⁻⁴ = x⁶. Answer: A

Which expression is equivalent to (x²)⁴?

A) x⁸    B) x⁶    C) x²    D) 8x²

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Power of a power: multiply exponents: x²ˣ⁴ = x⁸. Answer: A

Which expression is equivalent to x⁻³?

A) 1/x³    B) -x³    C) -1/x³    D) 1/(-3x)

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A negative exponent means reciprocal: x⁻³ = 1/x³. Answer: A

Which expression is equivalent to x^(1/2)?

A) √x    B) x²    C) 1/√x    D) 2x

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A fractional exponent of 1/2 represents a square root: x^(1/2) = √x. Answer: A

Which expression is equivalent to x^(2/3)?

A) ∛(x²)    B) √(x³)    C) (∛x)⁻²    D) 2x/3

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The denominator of the fractional exponent is the root, and the numerator is the power: x^(2/3) = ∛(x²). Answer: A

Which expression is equivalent to (2x³y²)²?

A) 4x⁶y⁴    B) 2x⁶y⁴    C) 4x⁵y⁴    D) 4x⁶y²

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Square each factor: 2² = 4, (x³)² = x⁶, (y²)² = y⁴, giving 4x⁶y⁴. Answer: A

Which expression is equivalent to √(18x⁴)?

A) 3x²√2    B) 3x√2    C) 9x²√2    D) 6x²√2

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18x⁴ = 9 · 2 · x⁴, and √(9x⁴) = 3x². So √(18x⁴) = 3x²√2. Answer: A

Which expression is equivalent to (x⁴y³)/(x²y)?

A) x²y²    B) x²y³    C) x⁶y⁴    D) x²y

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Subtract exponents for each base: x⁴⁻² = x², y³⁻¹ = y², giving x²y². Answer: A

Which expression is equivalent to (x⁻²y³)⁻¹?

A) x²/y³    B) x²y³    C) 1/(x²y³)    D) y³/x²

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Distribute the outer exponent: x⁻²ˣ⁻¹y³ˣ⁻¹ = x²y⁻³ = x²/y³. Answer: A

Which expression is equivalent to 5⁰ · x³?

A) x³    B) 0    C) 5x³    D) x⁰

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Any nonzero number to the 0 power is 1, so 5⁰ = 1, and 1 · x³ = x³. Answer: A

Which expression is equivalent to (x^(3/4))^(4/3)?

A) x    B) x^(9/16)    C) x^(7/12)    D) x²

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Multiply the exponents: (3/4)(4/3) = 1, so the result is x¹ = x. Answer: A

Which expression is equivalent to (x² − 4)/(x − 2), for x ≠ 2?

A) x + 2    B) x − 2    C) x² − 2    D) x + 4

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Factor the numerator: (x − 2)(x + 2)/(x − 2) = x + 2. Answer: A

Which expression is equivalent to (x² + 5x + 6)/(x + 2), for x ≠ -2?

A) x + 3    B) x + 2    C) x + 6    D) x − 3

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Factor the numerator: (x + 2)(x + 3)/(x + 2) = x + 3. Answer: A

Which expression is equivalent to (2x² − 8)/(x² − 4), for x ≠ ±2?

A) 2    B) x + 2    C) 2x    D) 2/(x − 2)

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Factor: 2(x² − 4)/(x² − 4) = 2, since (x² − 4) cancels entirely. Answer: A

Which expression is equivalent to (3x)/(x²) + (2)/(x), for x ≠ 0?

A) 5/x    B) 5/x²    C) 5x/x²    D) 5

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3x/x² = 3/x. Then 3/x + 2/x = 5/x. Answer: A

Which expression is equivalent to 1/(x − 1) + 1/(x + 1), for x ≠ ±1?

A) 2x/(x² − 1)    B) 2/(x² − 1)    C) 2x/(x + 1)    D) 1/(x² − 1)

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Common denominator (x − 1)(x + 1): (x + 1)/(x²−1) + (x − 1)/(x²−1) = 2x/(x² − 1). Answer: A

Which expression is equivalent to (x² − x)/(x), for x ≠ 0?

A) x − 1    B) x + 1    C) x² − 1    D) -1

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Factor: x(x − 1)/x = x − 1. Answer: A

Which expression is equivalent to (x²−1)/(x²+2x+1), for x ≠ -1?

A) (x − 1)/(x + 1)    B) (x + 1)/(x − 1)    C) x − 1    D) 1/(x + 1)

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Factor top and bottom: (x−1)(x+1)/(x+1)² = (x − 1)/(x + 1). Answer: A

Which expression is equivalent to (4x² − 1)/(2x − 1), for x ≠ 1/2?

A) 2x + 1    B) 2x − 1    C) 4x + 1    D) 2x

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4x² − 1 = (2x − 1)(2x + 1), so dividing by (2x − 1) leaves 2x + 1. Answer: A

Which expression is equivalent to (2/x) − (3/(x+1)), for x ≠ 0, -1?

A) (-x + 2)/(x(x+1))    B) (x + 2)/(x(x+1))    C) -1/(x(x+1))    D) (5x + 2)/(x(x+1))

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Common denominator x(x+1): [2(x+1) − 3x] / [x(x+1)] = (2x + 2 − 3x)/[x(x+1)] = (-x + 2)/[x(x+1)]. Answer: A

Which expression is equivalent to (x² + 2x)/(x² − 4), for x ≠ ±2?

A) x/(x − 2)    B) x/(x + 2)    C) (x+2)/(x−2)    D) x

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Factor top and bottom: x(x + 2) / [(x − 2)(x + 2)] = x/(x − 2). Answer: A

If a(x + b) = 4x + 12 for all values of x, what is the value of a + b?

A) 7    B) 6    C) 8    D) 16

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Distributing gives ax + ab = 4x + 12, so a = 4 and ab = 12, meaning b = 3. Then a + b = 7. Answer: A

Which expression is equivalent to (x + 3)² − (x − 3)²?

A) 12x    B) 6x    C) 12x + 18    D) 4x

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Expand both: (x² + 6x + 9) − (x² − 6x + 9) = 12x. Answer: A

If k(2x − 1) + 4 is equivalent to 8x + 0, what is the value of k?

A) 4    B) 3    C) 5    D) 2

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Distribute: 2kx − k + 4 = 8x + 0. Matching the x-coefficients: 2k = 8 → k = 4. Checking the constant term: -4 + 4 = 0, which matches. Answer: A

Which expression is equivalent to (x⁻¹ + y⁻¹)⁻¹?

A) xy/(x + y)    B) (x + y)/xy    C) x + y    D) xy

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1/x + 1/y = (y + x)/xy. Taking the reciprocal of that sum gives xy/(x + y). Answer: A

Which expression is equivalent to (x² − y²)/(x − y) · (1/(x + y)), for x ≠ ±y?

A) 1    B) x − y    C) x + y    D) 0

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(x²−y²)/(x−y) simplifies to (x+y). Multiplying by 1/(x+y) gives (x+y)/(x+y) = 1. Answer: A

If (x + a)(x + b) = x² + 9x + 20 for all x, what is a² + b²?

A) 41    B) 25    C) 20    D) 89

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a and b multiply to 20 and add to 9, so {a, b} = {4, 5}. Then a² + b² = 16 + 25 = 41. Answer: A

Which expression is equivalent to √(x² ), for x < 0?

A) -x    B) x    C) |x|²    D) x²

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√(x²) = |x|. Since x is negative, |x| = -x. Answer: A

Which expression is equivalent to (x³ − 8)/(x − 2), for x ≠ 2?

A) x² + 2x + 4    B) x² − 2x + 4    C) x² + 4    D) x² − 4

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This is a difference of cubes: x³ − 8 = (x − 2)(x² + 2x + 4). Dividing by (x − 2) leaves x² + 2x + 4. Answer: A

If m and n are constants and mx² + nx − 3 is equivalent to (2x − 1)(x + 3), what is the value of m + n?

A) 7    B) 5    C) 8    D) 2

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Expand: (2x − 1)(x + 3) = 2x² + 6x − x − 3 = 2x² + 5x − 3. So m = 2 and n = 5, giving m + n = 7. Answer: A

Which expression is equivalent to (x/(x−1)) − (1/(x−1)), for x ≠ 1?

A) 1    B) x    C) x − 1    D) 0

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Same denominator, so combine numerators: (x − 1)/(x − 1) = 1. Answer: A

What does it mean for two expressions to be equivalent?

Two expressions are equivalent if they give the same value for every valid input of the variable, not just for a single convenient number.

Is plugging in numbers a reliable strategy on the SAT?

Yes, provided that you select an odd test result and compare it to each of the remaining response options. This is because 0 or 1 can coincidentally make many choices match..

How do I know which factoring pattern to use?

Prior to attempting generic trinomial factoring, search for a difference of squares (a² − b²) or a perfect square trinomial (a² ± 2ab + b²)..

Can I cancel terms in a rational expression the same way I cancel factors?

No, only factors that have been multiplied can be cancelled. Until the equation is entirely factored, terms that are added or deleted must remain in the numerator or denominator.

How many equivalent expression questions should I practice before the SAT?

Before the test, most students benefit from 50–70 mixed practice questions that include factoring, simplification, exponent rules, and rational expressions.