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Polynomial Multiplication Mastery

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Polynomial Multiplication Mastery

Multiply each polynomial and simplify by combining like terms. Show your work for long-answer questions. A term such as x² means x multiplied by x.

Multiply binomials

Use the distributive property or FOIL, then collect like terms.

1.Expand and simplify: (x + 4)(x + 7).
2.Choose the correct expansion of (2x + 3)(x − 5).
  • 2x² − 7x − 15
  • 2x² + 7x − 15
  • 2x² − 10x + 15
  • 2x² − 2x − 15
3.Expand and simplify: (3x − 2)(x + 6). Show how you combine the middle terms.

×

x

3

x

x²

3x

2

2x

6

4.Use the area model above to expand (x + 2)(x + 3). Add the four cell products and simplify.

Distribute across every term

Multiply each term in the first polynomial by every term in the second polynomial.

5.Expand and simplify: (x + 2)(x² + 3x + 5).
6.Fill in the missing coefficient: (x − 1)(x² + 4x + 7) = x³ + 3x² + x − 7.
7.Expand and simplify: (2x + 3)(x² + x + 4).

Spot the structure

Check each product carefully: signs and like terms matter.

8.True or false? (x + 5)(x − 5) = x² + 25. If false, write the correct product.
TrueFalse
9.Match each product to its simplified result.
  • (x + 2)(x + 6)
  • (x − 3)(x + 3)
  • (2x − 1)(x + 4)
  • 2x² + 7x − 4
  • x² + 8x + 12
  • x² − 9
10.A rectangular sports-day banner has side lengths (x + 4) feet and (x + 2) feet. Write a simplified polynomial for its area in square feet.
11.Challenge: Expand and simplify (3x + 2)(2x² + 5x + 1). Show the terms before combining like terms.

3 printable pages

  • Polynomial Multiplication Mastery, page 1 of 3: Multiply binomials

    Page 1

  • Polynomial Multiplication Mastery, page 2 of 3: Distribute across every term, Spot the structure

    Page 2

  • Polynomial Multiplication Mastery, page 3 of 3: 11. Challenge: Expand and simplify (3x + 2)(2x² + 5x + 1). Show the terms before…

    Page 3

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