Lesson Worksheet: Factoring Perfect Square Trinomials Mathematics • 9th Grade

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In this worksheet, we will practice factoring a perfect square trinomial expression.

Q1:

For which values of 𝑘 is 16𝑥+𝑘𝑥+81 a perfect square?

  • A13,−13
  • B72,−72
  • C36,−36
  • D26,−26

Q2:

Which of the following is a perfect square?

  • A𝑥+81
  • B𝑥−18𝑥−81
  • C𝑥−81
  • D𝑥−9𝑥+81
  • E𝑥−18𝑥+81

Q3:

Complete the quadratic expression 9𝑥+144 to make a perfect square.

  • A+72𝑥
  • B+72𝑥−72𝑥or
  • C+72𝑥−72𝑥or
  • D+30𝑥
  • E+36𝑥−36𝑥or

Q4:

Factorize fully 𝑥−10𝑥𝑦+25𝑦.

  • A(−5𝑥+𝑦)
  • B(1−5𝑥𝑦)
  • C(1+5𝑥𝑦)
  • D(𝑥−5𝑦)
  • E(𝑥+5𝑦)

Q5:

Factorize fully 81𝑚+18𝑚+1.

  • A(9𝑚+1)(9𝑚−1)
  • B(𝑚−9)
  • C(9𝑚+1)
  • D(9𝑚+1)(𝑚+9)
  • E(𝑚+9)

Q6:

Factorize fully 64𝑦𝑥−64𝑦𝑥+16𝑦.

  • A16(8𝑥+4)(8𝑥−4)
  • B16𝑦(2𝑥+1)
  • C16𝑦(8−4𝑥)
  • D16𝑥(8−4𝑦)
  • E16𝑦(2𝑥−1)

Q7:

Factorize fully 24𝑥𝑦+3𝑥+48𝑦.

  • A3(𝑥+4𝑦)
  • B(𝑥+𝑦)
  • C3(4𝑥+𝑦)
  • D(𝑥+4𝑦+3)
  • E(4𝑥+𝑦)

Q8:

By factorizing or otherwise, evaluate (10.1)−4.2×10.1+(2.1).

Q9:

By factorizing or otherwise, evaluate (97)+6×97+9.

Q10:

Given that 𝑥+2𝑥𝑦+𝑦=81, what are the possible values of 𝑥+𝑦?

  • A18,−18
  • B81,−81
  • C9,−9
  • D40,−40

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