Worksheet: Difference of Two Squares

In this worksheet, we will practice determining when a quadratic is a difference of two squares and then using this property to factor the expression and multiplying the sum of two terms by their difference to get the polynomial known as the difference of two squares.

Q1:

Factorize fully 100𝑥121𝑦.

  • A(11𝑥10𝑦)
  • B(11𝑥+10𝑦)(11𝑥10𝑦)
  • C21(𝑥+𝑦)(𝑥𝑦)
  • D(10𝑥11𝑦)
  • E(10𝑥+11𝑦)(10𝑥11𝑦)

Q2:

Factorize fully 9𝑚64𝑛.

  • A11𝑚+𝑛𝑚𝑛
  • B8𝑚+3𝑛8𝑚3𝑛
  • C3𝑚+8𝑛3𝑚8𝑛
  • D8𝑚3𝑛
  • E(3𝑚8𝑛)

Q3:

Factorize fully 16𝑎𝑏49.

  • A4𝑎𝑏+74𝑎𝑏7
  • B(4𝑎+7𝑏)(4𝑎7𝑏)
  • C(4𝑎𝑏7)
  • D(4𝑎𝑏+7)(4𝑎𝑏7)
  • E(4𝑎7𝑏)

Q4:

Factorize fully 49𝑎64𝑏𝑐.

  • A7𝑎+8𝑏𝑐7𝑎8𝑏𝑐
  • B7𝑎8𝑏𝑐
  • C(7𝑎+8𝑏𝑐)(7𝑎8𝑏𝑐)
  • D(7𝑎8𝑏𝑐)
  • E49𝑎+64𝑏𝑐49𝑎64𝑏𝑐

Q5:

Find the solution set of 𝑥1,089=0 in .

  • A{33}
  • B{0,33}
  • C{33,33}
  • D{33}

Q6:

Factorize fully (𝑥+4𝑦+3)(𝑥4𝑦3).

  • A4𝑦(4𝑥+3)
  • B(4𝑥3𝑦)
  • C4(4𝑦+3𝑥)
  • D4𝑥(4𝑦+3)
  • E(4𝑥𝑦3)

Q7:

If 𝑥𝑦=8, what is the value of (𝑥+3𝑦)(𝑥3𝑦)?

Q8:

If 𝑥81𝑦=24 and 𝑥+9𝑦=6, what is the value of 5𝑥45𝑦?

Q9:

If 𝑥16𝑦=80 and 𝑥+4𝑦=5, what is the value of 4𝑦𝑥?

Q10:

Factorize fully 4𝑏(7𝑎𝑏)𝑎(7𝑎𝑏).

  • A(2𝑎+𝑏)(7𝑏𝑎)(7𝑏+𝑎)
  • B(7𝑎𝑏)(2𝑏𝑎)
  • C(7𝑏𝑎)(2𝑏+𝑎)(2𝑏𝑎)
  • D(7𝑎𝑏)(4𝑏+𝑎)(4𝑏𝑎)
  • E(7𝑎𝑏)(2𝑏+𝑎)(2𝑏𝑎)

Q11:

Factorize fully 𝑥𝑦49𝑥𝑦.

  • A𝑥𝑦(𝑥+7𝑦)(𝑥7𝑦)
  • B𝑥+7𝑦𝑥7𝑦
  • C𝑥𝑦𝑥+7𝑦𝑥7𝑦
  • D𝑥𝑦𝑥7𝑦
  • E𝑥𝑦𝑥+7𝑦𝑥7𝑦

Q12:

Factorize fully 𝑦256.

  • A(𝑦4)(𝑦+4)(𝑦16)
  • B(𝑦+4)(𝑦4)
  • C(𝑦4)(𝑦+4)(𝑦+16)
  • D(𝑦4)(𝑦+4)
  • E(𝑦16)

Q13:

By factorizing or otherwise, evaluate (7.46)(2.54).

Q14:

If 𝑎+3𝑏=9(𝑎3𝑏)=27, what is the value of 𝑎9𝑏?

Q15:

Factorize fully 16𝑎4925𝑏64.

  • A4𝑎49+5𝑏644𝑎495𝑏64
  • B16𝑎49+25𝑏6416𝑎4925𝑏64
  • C4𝑎75𝑏8
  • D4𝑎7+5𝑏84𝑎75𝑏8
  • E4𝑎7+5𝑏84𝑎75𝑏8

Q16:

By considering the difference of two squares, evaluate 91×89 without a calculator.

Q17:

If 𝑥>10𝑦, 𝑥20𝑥𝑦+100𝑦=36, and 𝑥+10𝑦=2, what is the value of 𝑥100𝑦?

Q18:

Factorize fully 9𝑥121𝑦𝑧.

  • A(11𝑥+3𝑦𝑧)(11𝑥3𝑦𝑧)
  • B(3𝑥11𝑦𝑧)
  • C(3𝑥+11𝑦𝑧)(3𝑥11𝑦𝑧)
  • D(11𝑥3𝑦𝑧)
  • E14(𝑥+𝑦𝑧)(𝑥𝑦𝑧)

Q19:

If 25𝑥16𝑦=5𝑥+4𝑦, what is the value of 5𝑥4𝑦?

Q20:

By considering the difference of two squares, find the value of 𝑥 for which 3919=20𝑥.

Q21:

Factorize fully 6449𝑛.

  • A(87𝑛)
  • B(7𝑛8)
  • C(8𝑛+7)(8𝑛7)
  • D(8+7𝑛)(87𝑛)
  • E(7𝑛+8)(7𝑛8)

Q22:

Factorize fully 625𝑥16𝑦.

  • A4𝑥+25𝑦4𝑥25𝑦
  • B25𝑥+4𝑦25𝑥4𝑦
  • C25𝑥+4𝑦25𝑥4𝑦
  • D25𝑥4𝑦
  • E3(25𝑥4𝑦)

Q23:

Factorize fully and evaluate (6.862)(3.138).

Q24:

Factorize fully 2𝑚50𝑚𝑛.

  • A2𝑚(5𝑚+𝑛)(5𝑚𝑛)
  • B2(𝑚+5𝑛)
  • C2(5𝑚+𝑛)
  • D2𝑚(𝑚+5𝑛)(𝑚5𝑛)
  • E(𝑚+5𝑛)(𝑚5𝑛)

Q25:

Factorize fully 36𝑎(3𝑎+7𝑏).

  • A(33𝑎+43𝑏)(39𝑎+43𝑏)
  • B(33𝑎+29𝑏)(39𝑎+43𝑏)
  • C(3𝑎+13𝑏)(9𝑎+13𝑏)
  • D(3𝑎7𝑏)(9𝑎+7𝑏)
  • E(3𝑎𝑏)

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