Lesson Worksheet: Multiplying Polynomials Mathematics

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

Q1:

Expand the product (𝑥+4)(𝑥+6).

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

Q2:

Expand (2𝑥+5).

  • A4𝑥+10𝑥+25
  • B4𝑥+10𝑥+10
  • C4𝑥+20𝑥+10
  • D4𝑥−20𝑥+25
  • E4𝑥+20𝑥+25

Q3:

Expand and simplify (−2𝑥−4𝑦)(2𝑥−𝑦).

  • A−4𝑥−6𝑥𝑦−4𝑦
  • B−4𝑥−10𝑥𝑦+4𝑦
  • C−4𝑥+6𝑥𝑦+4𝑦
  • D−4𝑥−6𝑥𝑦+4𝑦
  • E4𝑥−10𝑥𝑦+4𝑦

Q4:

Simplify 3𝑎−22𝑎+4.

  • A6𝑎−12𝑎−4𝑎−8
  • B6𝑎−12𝑎+4𝑎−8
  • C6𝑎+12𝑎−4𝑎+8
  • D6𝑎+12𝑎−4𝑎−8
  • E6𝑎+12𝑎+4𝑎−8

Q5:

Expand and simplify (𝑥−2𝑦+3)(2𝑥+𝑦).

  • A2𝑥−3𝑥𝑦−2𝑦+5𝑥+3𝑦
  • B2𝑥−3𝑥𝑦−2𝑦+6𝑥+3𝑦
  • C2𝑥−4𝑥𝑦+6𝑥
  • D𝑥𝑦−2𝑦+3𝑦
  • E2𝑥−5𝑥𝑦−2𝑦+6𝑥+3𝑦

Q6:

Determine which of the following expressions is equivalent to (𝑥−𝑦).

  • A𝑥−3𝑥𝑦+3𝑥𝑦+𝑦
  • B𝑥+3𝑥𝑦−3𝑥𝑦+𝑦
  • C𝑥+3𝑥𝑦−3𝑥𝑦−𝑦
  • D𝑥−𝑦
  • E𝑥−3𝑥𝑦+3𝑥𝑦−𝑦

Q7:

Expand and simplify (𝑥−1)(2𝑥+5)(𝑥+1).

  • A2𝑥−5𝑥−2𝑥−5
  • B2𝑥−5𝑥−2𝑥+5
  • C2𝑥+5𝑥−2𝑥−5
  • D2𝑥+5𝑥+2𝑥+5
  • E2𝑥+5𝑥+2𝑥−5

Q8:

A rectangle with dimensions (𝑥−𝑦) 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.

  • A𝑥−𝑦+𝑥−𝑦
  • B3𝑥+4𝑥𝑦+2𝑦+5𝑥+4𝑦
  • C𝑥+𝑦+𝑥+𝑦
  • D3𝑥−4𝑥𝑦−2𝑦−5𝑥−4𝑦
  • E4𝑥+4𝑥𝑦+𝑦+6𝑥+3𝑦

Q9:

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
  • B24𝑥−4𝑥 cm3
  • C24𝑥+𝑥 cm3
  • D12𝑥+2𝑥 cm3
  • E24𝑥+1 cm3

Q10:

If (2𝑥−𝑦)(2𝑥−5𝑦)(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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