Worksheet: Expanding an Expression to a Difference of Two Squares

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)(𝑥1).

  • A𝑥+1
  • B𝑥2𝑥1
  • C𝑥+2𝑥1
  • D𝑥1
  • E𝑥+2𝑥+1

Q2:

Use the difference of two squares identity to expand (3𝑎+7)(3𝑎7).

  • A6𝑎14
  • B9𝑎7
  • C9𝑎49
  • D9𝑎49
  • E3𝑎49

Q3:

If 𝑥𝑎=(𝑥+5)(𝑥5), what is the value of 𝑎?

Q4:

Expand the product (2𝑚+𝑛)(2𝑚𝑛).

  • A4𝑚+2𝑚𝑛+𝑛
  • B4𝑚+2𝑚𝑛𝑛
  • C4𝑚2𝑚𝑛+𝑛
  • D4𝑚𝑛
  • E4𝑚+𝑛

Q5:

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

Q6:

Complete the following: 𝑥=(𝑥5)(𝑥+5).

Q7:

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

Q8:

If 𝑥+𝑙25=(𝑥+5)(𝑥5), what is the value of 𝑙?

Q9:

Given that 𝑛+𝑚=5 and 𝑛𝑚=45, find 𝑛𝑚.

Q10:

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

Q11:

What is the value of 7+373?

Q12:

Simplify (4𝑧+7)(4𝑧7).

  • A16𝑧5649
  • B16𝑧+49
  • C16𝑧+56+49
  • D16𝑧+5649
  • E16𝑧49

Q13:

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

Q14:

Given that 𝑥𝑦=62 and 𝑥𝑦=31, find 𝑥+𝑦.

  • A6231
  • B2
  • C231
  • D3162

Q15:

Expand (2𝑥3)(2𝑥+3).

  • A4𝑥9
  • B4𝑥9
  • C4𝑥+9
  • D4𝑥+12𝑥9
  • E4𝑥+6𝑥9

Q16:

Simplify 3+232.

Q17:

What is the area of a rectangle of length (𝑥+14) cm and width (𝑥14) cm?

  • A𝑥+196 cm2
  • B𝑥196 cm2
  • C2𝑥 cm2
  • D(𝑥14) cm2
  • E(𝑥+14) cm2

Q18:

If 𝑥𝑎=(𝑥+10)(𝑥10), what is the value of 𝑎?

Q19:

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

Q20:

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

Q21:

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

Q22:

Given that 𝑥+𝑧=3 and 𝑥𝑧=3, find 𝑥𝑧.

Q23:

If 𝑥+𝑙144=(𝑥+12)(𝑥12), what is the value of 𝑙?

Q24:

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

Q25:

Use the identity (𝑥𝑦)(𝑥+𝑦)=𝑥𝑦 to evaluate 3331 without using a calculator.

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