Lesson Worksheet: Multiplying Polynomials Mathematics

In this worksheet, we will practice multiplying polynomial expressions together by expanding the parentheses.


Expand the product (𝑥+4)(𝑥+6).

  • A𝑥+24
  • B𝑥+10𝑥
  • C11𝑥+24
  • D𝑥+10𝑥+24
  • E𝑥+34𝑥


Expand (2𝑥+5).

  • A4𝑥+10𝑥+25
  • B4𝑥+10𝑥+10
  • C4𝑥+20𝑥+10
  • D4𝑥20𝑥+25
  • E4𝑥+20𝑥+25


Expand and simplify (2𝑥4𝑦)(2𝑥𝑦).

  • A4𝑥6𝑥𝑦4𝑦
  • B4𝑥10𝑥𝑦+4𝑦
  • C4𝑥+6𝑥𝑦+4𝑦
  • D4𝑥6𝑥𝑦+4𝑦
  • E4𝑥10𝑥𝑦+4𝑦


Simplify 3𝑎22𝑎+4.

  • A6𝑎12𝑎4𝑎8
  • B6𝑎12𝑎+4𝑎8
  • C6𝑎+12𝑎4𝑎+8
  • D6𝑎+12𝑎4𝑎8
  • E6𝑎+12𝑎+4𝑎8


Expand and simplify (𝑥2𝑦+3)(2𝑥+𝑦).

  • A2𝑥3𝑥𝑦2𝑦+5𝑥+3𝑦
  • B2𝑥3𝑥𝑦2𝑦+6𝑥+3𝑦
  • C2𝑥4𝑥𝑦+6𝑥
  • D𝑥𝑦2𝑦+3𝑦
  • E2𝑥5𝑥𝑦2𝑦+6𝑥+3𝑦


Determine which of the following expressions is equivalent to (𝑥𝑦).

  • A𝑥3𝑥𝑦+3𝑥𝑦+𝑦
  • B𝑥+3𝑥𝑦3𝑥𝑦+𝑦
  • C𝑥+3𝑥𝑦3𝑥𝑦𝑦
  • D𝑥𝑦
  • E𝑥3𝑥𝑦+3𝑥𝑦𝑦


Expand and simplify (𝑥1)(2𝑥+5)(𝑥+1).

  • A2𝑥5𝑥2𝑥5
  • B2𝑥5𝑥2𝑥+5
  • C2𝑥+5𝑥2𝑥5
  • D2𝑥+5𝑥+2𝑥+5
  • E2𝑥+5𝑥+2𝑥5


A rectangle with dimensions (𝑥𝑦) and (𝑥+𝑦+1) is cut out from a larger rectangle with dimensions (2𝑥+𝑦+3) and (2𝑥+𝑦). Find a simplified expression for the shaded area.

  • A𝑥𝑦+𝑥𝑦
  • B3𝑥+4𝑥𝑦+2𝑦+5𝑥+4𝑦
  • C𝑥+𝑦+𝑥+𝑦
  • D3𝑥4𝑥𝑦2𝑦5𝑥4𝑦
  • E4𝑥+4𝑥𝑦+𝑦+6𝑥+3𝑦


A rectangular prism has a height of 6𝑥+1 cm and a square-shaped base with a side length of 2𝑥 cm. Find its volume in terms of 𝑥.

  • A24𝑥+4𝑥 cm3
  • B24𝑥4𝑥 cm3
  • C24𝑥+𝑥 cm3
  • D12𝑥+2𝑥 cm3
  • E24𝑥+1 cm3


If (2𝑥𝑦)(2𝑥5𝑦)(3𝑥+2𝑦)=𝑎𝑥+𝑏𝑥𝑦+𝑐𝑥𝑦+𝑑𝑦, what are the values of 𝑎, 𝑏, 𝑐, and 𝑑?

  • A𝑎=10, 𝑏=9, 𝑐=28, 𝑑=12
  • B𝑎=12, 𝑏=28, 𝑐=9, 𝑑=10
  • C𝑎=13, 𝑏=27, 𝑐=8, 𝑑=11
  • D𝑎=13, 𝑏=27, 𝑐=8, 𝑑=11
  • E𝑎=12, 𝑏=28, 𝑐=9, 𝑑=10

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