Lesson Worksheet: Expanding an Expression to a Difference of Two Squares Mathematics • 9th Grade

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In this worksheet, we will practice multiplying the sum of two terms by their difference to get the polynomial known as the difference of two squares.

Q1:

Expand the product (𝑥+1)(𝑥−1).

  • A𝑥+1
  • B𝑥−2𝑥−1
  • C𝑥+2𝑥−1
  • D𝑥−1
  • E𝑥+2𝑥+1

Q2:

Use the difference of two squares identity to expand (3𝑎+7)(3𝑎−7).

  • A6𝑎−14
  • B9𝑎−7
  • C9𝑎−49
  • D9𝑎−49
  • E3𝑎−49

Q3:

If 𝑥−𝑎=(𝑥+5)(𝑥−5), what is the value of 𝑎?

Q4:

Expand the product (2𝑚+𝑛)(2𝑚−𝑛).

  • A4𝑚+2𝑚𝑛+𝑛
  • B4𝑚+2𝑚𝑛−𝑛
  • C4𝑚−2𝑚𝑛+𝑛
  • D4𝑚−𝑛
  • E4𝑚+𝑛

Q5:

If 𝑥−𝑦=9 and 𝑥+𝑦=10, what is the value of 𝑥−𝑦?

Q6:

Complete the following: 𝑥−=(𝑥−5)(𝑥+5).

Q7:

If 𝑥+𝑦=2 and 𝑥−𝑦=6, what is the value of 𝑥−𝑦?

Q8:

If 𝑥+𝑙−25=(𝑥+5)(𝑥−5), what is the value of 𝑙?

Q9:

Given that 𝑛+𝑚=5 and 𝑛−𝑚=45, find 𝑛−𝑚.

Q10:

If 𝑚−𝑛=64 and 𝑚+𝑛=4, what is the value of 𝑚−𝑛?

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