Lesson Worksheet: Difference of Two Squares Mathematics • 9th Grade

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In this worksheet, we will practice factoring the difference of two squares and applying the result to evaluate numerical expressions.

Q1:

Factor the expression 𝑥−49.

  • A(2𝑥+7)
  • B(𝑥−7)
  • C(𝑥+7)(𝑥−7)
  • D(𝑥+49)(𝑥−49)
  • E(2𝑥−7)

Q2:

Factorize fully 100𝑥−121𝑦.

  • A(11𝑥−10𝑦)
  • B(11𝑥+10𝑦)(11𝑥−10𝑦)
  • C21(𝑥+𝑦)(𝑥−𝑦)
  • D(10𝑥−11𝑦)
  • E(10𝑥+11𝑦)(10𝑥−11𝑦)

Q3:

Factorize fully 64𝑥−81.

  • A(9𝑥+8)(9𝑥−8)
  • B(𝑥−72)
  • C(8𝑥+9)(8𝑥−9)
  • D(𝑥+72)(𝑥−72)
  • E(8𝑥−9)

Q4:

Factorize fully 9𝑚−64𝑛.

  • A11𝑚+𝑛𝑚−𝑛
  • B8𝑚+3𝑛8𝑚−3𝑛
  • C3𝑚+8𝑛3𝑚−8𝑛
  • D8𝑚−3𝑛
  • E(3𝑚−8𝑛)

Q5:

Factorize fully 49𝑎−64𝑏𝑐.

  • A7𝑎+8𝑏𝑐7𝑎−8𝑏𝑐
  • B7𝑎−8𝑏𝑐
  • C(7𝑎+8𝑏𝑐)(7𝑎−8𝑏𝑐)
  • D(7𝑎−8𝑏𝑐)
  • E49𝑎+64𝑏𝑐49𝑎−64𝑏𝑐

Q6:

Factorize fully (𝑥+4𝑦+3)−(𝑥−4𝑦−3).

  • A4𝑦(4𝑥+3)
  • B(4𝑥−3𝑦)
  • C4(4𝑦+3𝑥)
  • D4𝑥(4𝑦+3)
  • E(4𝑥𝑦−3)

Q7:

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

Q8:

By factorizing or otherwise, evaluate (77)−(23).

Q9:

By factoring or otherwise, evaluate 5×(8.85)−5×(6.85).

Q10:

The length of the hypotenuse of a right triangle is 64 cm and the length of one of the other sides is 59 cm. Find the area of the square drawn on that unknown side.

This lesson includes 51 additional questions and 480 additional question variations for subscribers.

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