Worksheet: Expanding an Expression to a Difference of Two Squares

Download

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?

Q11:

What is the value of √7+√3√7−√3?

Q12:

Simplify (4𝑧+7)(4𝑧−7).

  • A16𝑧−56−49
  • B16𝑧+49
  • C16𝑧+56+49
  • D16𝑧+56−49
  • E16𝑧−49

Q13:

Given that 𝑥=2 and 𝑦=√3, find the value of 3(𝑥+𝑦)(𝑥−𝑦).

Q14:

Given that 𝑥−𝑦=62 and 𝑥−𝑦=√31, find 𝑥+𝑦.

  • A62√31
  • B√2
  • C2√31
  • D√3162

Q15:

Expand (2𝑥−3)(2𝑥+3).

  • A−4𝑥−9
  • B4𝑥−9
  • C4𝑥+9
  • D4𝑥+12𝑥−9
  • E4𝑥+6𝑥−9

Q16:

Simplify √3+2√3−2.

Q17:

What is the area of a rectangle of length (𝑥+14) cm and width (𝑥−14) cm?

  • A𝑥+196 cm2
  • B𝑥−196 cm2
  • C2𝑥 cm2
  • D(𝑥−14) cm2
  • E(𝑥+14) cm2

Q18:

If 𝑥−𝑎=(𝑥+10)(𝑥−10), what is the value of 𝑎?

Q19:

If 𝑎−𝑏=10 and 𝑎+𝑏=18, what is the value of 𝑎−𝑏?

Q20:

If 𝑚−𝑛=5 and 𝑚+𝑛=14, what is the value of 𝑚−𝑛?

Q21:

If 𝑥+𝑦=9 and 𝑥−𝑦=6, what is the value of 𝑥−𝑦?

Q22:

Given that 𝑥+𝑧=3 and 𝑥−𝑧=3, find 𝑥−𝑧.

Q23:

If 𝑥+𝑙−144=(𝑥+12)(𝑥−12), what is the value of 𝑙?

Q24:

Using the difference of two squares, evaluate 21×19 without a calculator.

Q25:

Use the identity (𝑥−𝑦)(𝑥+𝑦)=𝑥−𝑦 to evaluate 33−31 without using a calculator.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.