Grade 9 · Algebra & functions

Polynomial expression multiplication (SAT) practice

Polynomial expression multiplication (SAT) is a grade 9 math skill aligned to Common Core standard HSA.APR.A.1: understand that polynomials form a system analogous to the integers: they are closed under addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 polynomial expression multiplication (sat) problems our math games drill.

CCSS HSA.APR.A.110 questions in the bank
Sample questions

Try 8 for free

Question 1easy

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

Expand: (x+2)(x+5)=x2+5x+2x+10=x2+7x+10(x + 2)(x + 5) = x^2 + 5x + 2x + 10 = x^2 + 7x + 10. Then add 33: x2+7x+10+3=x2+7x+13x^2 + 7x + 10 + 3 = x^2 + 7x + 13.

Question 2easy

Which expression is equivalent to (x−1)(x−6)(x - 1)(x - 6)?

Expand: (x−1)(x−6)=x2−6x−x+6=x2−7x+6(x - 1)(x - 6) = x^2 - 6x - x + 6 = x^2 - 7x + 6.

Question 3easy

Which expression is equivalent to (x+3)(x+3)−9(x + 3)(x + 3) - 9?

Expand: (x+3)(x+3)=x2+6x+9(x + 3)(x + 3) = x^2 + 6x + 9. Then subtract 99: x2+6x+9−9=x2+6xx^2 + 6x + 9 - 9 = x^2 + 6x.

Question 4easy

Which expression is equivalent to (x−8)(x+1)+7(x - 8)(x + 1) + 7?

Expand: (x−8)(x+1)=x2+x−8x−8=x2−7x−8(x - 8)(x + 1) = x^2 + x - 8x - 8 = x^2 - 7x - 8. Then add 77: x2−7x−8+7=x2−7x−1x^2 - 7x - 8 + 7 = x^2 - 7x - 1.

Question 5medium

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

Expand: (2x+1)(x−3)=2x2−6x+x−3=2x2−5x−3(2x + 1)(x - 3) = 2x^2 - 6x + x - 3 = 2x^2 - 5x - 3. Then add 44: 2x2−5x−3+4=2x2−5x+12x^2 - 5x - 3 + 4 = 2x^2 - 5x + 1.

Question 6medium

Which expression is equivalent to (x−5)(x+2)+10(x - 5)(x + 2) + 10?

Expand: (x−5)(x+2)=x2+2x−5x−10=x2−3x−10(x - 5)(x + 2) = x^2 + 2x - 5x - 10 = x^2 - 3x - 10. Then add 1010: x2−3x−10+10=x2−3xx^2 - 3x - 10 + 10 = x^2 - 3x.

Question 7medium

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

Expand: (x−2)(x+7)=x2+7x−2x−14=x2+5x−14(x - 2)(x + 7) = x^2 + 7x - 2x - 14 = x^2 + 5x - 14. Then subtract 55: x2+5x−14−5=x2+5x−19x^2 + 5x - 14 - 5 = x^2 + 5x - 19.

Question 8medium

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

Expand: (3x−1)(x+2)=3x2+6x−x−2=3x2+5x−2(3x - 1)(x + 2) = 3x^2 + 6x - x - 2 = 3x^2 + 5x - 2.

Tests that cover polynomial expression multiplication (sat):
SBACACTPARCCNY State MathNC EOG/EOC
More Grade 9 skills:
Polynomial combining like terms (SAT)Quadratic distinct real solutions countMonomial expression multiplication (SAT)Quadratic formulaLiteral equations (SAT)Quadratic minimum x-valueLinear systems by substitution (SAT)Radical to exponent conversionsAll Grade 9 practice →

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