Lesson Worksheet: Factoring Perfect-Square Trinomials Mathematics

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:

Complete the expression 16𝑥+𝑦 to make a perfect square.

  • A+8𝑥𝑦8𝑥𝑦or
  • B+10𝑥𝑦10𝑥𝑦or
  • C+4𝑥𝑦4𝑥𝑦or
  • D+8𝑥𝑦8𝑥𝑦or

Q3:

Which of the following is a perfect square?

  • A𝑥+81
  • B𝑥18𝑥81
  • C𝑥81
  • D𝑥9𝑥+81
  • E𝑥18𝑥+81

Q4:

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

  • A+72𝑥
  • B+72𝑥72𝑥or
  • C+72𝑥72𝑥or
  • D+30𝑥
  • E+36𝑥36𝑥or

Q5:

If 9𝑦+30𝑦+𝑏 is a perfect square, what is the value of 𝑏?

Q6:

Complete the expression 60𝑥+25 to make a perfect square.

  • A36𝑥
  • B12𝑥
  • C12𝑥
  • D36𝑥
  • E6𝑥

Q7:

Complete the expression 425𝑎+19𝑏 to make a perfect square.

  • A±415𝑎𝑏
  • B+45𝑎𝑏
  • C+25𝑎𝑏
  • D±215𝑎𝑏
  • E±415𝑎𝑏

Q8:

If 𝑘𝑦24𝑦+9 is a perfect square, what is the value of 𝑘?

Q9:

Factorize fully 9𝑥+36𝑥𝑦+36𝑦.

  • A9(2𝑥+𝑦)
  • B9(𝑥+2𝑦)
  • C(𝑥+2𝑦)
  • D9(𝑦+2𝑥)
  • E9(𝑥+2𝑦)

Q10:

Factorize fully 𝑥10𝑥𝑦+25𝑦.

  • A(5𝑥+𝑦)
  • B(15𝑥𝑦)
  • C(1+5𝑥𝑦)
  • D(𝑥5𝑦)
  • E(𝑥+5𝑦)

Q11:

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

Q12:

Factorize fully 81𝑚+18𝑚+1.

  • A(9𝑚+1)(9𝑚1)
  • B(𝑚9)
  • C(9𝑚+1)
  • D(9𝑚+1)(𝑚+9)
  • E(𝑚+9)

Q13:

Factorize fully 4(𝑥7)16(𝑥7)(𝑦6)+16(𝑦6).

  • A(2𝑥4𝑦38)
  • B(2𝑥4𝑦)
  • C(2𝑥4𝑦+10)
  • D2𝑥4𝑦+10
  • E(𝑥+𝑦2)

Q14:

Complete the expression 81𝑥+90𝑥𝑦+ to make a perfect square.

  • A25𝑦
  • B20𝑦
  • C25𝑦
  • D9𝑦
  • E25𝑦

Q15:

Factorize fully 4981𝑥+89𝑥+1649.

  • A79𝑥27
  • B79𝑥+47
  • C79𝑥+47
  • D79𝑥+27
  • E79𝑥47

Q16:

Expand and simplify 5𝑥(5𝑥+18𝑦)+81𝑦, then factorize the result.

  • A(5𝑥9𝑦)
  • B(5𝑥+9)
  • C(5𝑥+8)
  • D(5𝑥+8𝑦)
  • E(5𝑥+9𝑦)

Q17:

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

Q18:

Factorize fully 0.16𝑏+7.2𝑏+81.

  • A(0.4𝑏+9)
  • B(0.2𝑏+9)
  • C(0.2+9𝑏)
  • D(0.4+9𝑏)
  • E(0.4(𝑏+9))

Q19:

Factorize fully 481𝑥43𝑥+9.

  • A29𝑥+329𝑥3
  • B29𝑥3
  • C3𝑥29
  • D(9𝑥3)
  • E3𝑥+293𝑥29

Q20:

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

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

Q21:

Factorize fully 𝑎+6𝑎+9𝑎.

  • A(𝑎+3)
  • B𝑎(𝑎+3)
  • C𝑎(3𝑎+1)
  • D𝑎(3𝑎+1)(3𝑎1)
  • E𝑎(3𝑎+1)

Q22:

Factorize fully 64𝑦𝑥64𝑦𝑥+16𝑦.

  • A16(8𝑥+4)(8𝑥4)
  • B16𝑦(2𝑥+1)
  • C16𝑦(84𝑥)
  • D16𝑥(84𝑦)
  • E16𝑦(2𝑥1)

Q23:

Write all possible expressions for 𝑘 such that 𝑥+𝑘+4𝑦 is a perfect square.

  • A4,4
  • B2𝑥𝑦,2𝑥𝑦
  • C4𝑥𝑦,4𝑥𝑦
  • D6𝑥𝑦,6𝑥𝑦

Q24:

Factorize fully (𝑎+4𝑏)+14𝑐(𝑎+4𝑏)+49𝑐.

  • A𝑎+4𝑏7𝑐
  • B𝑎+4𝑏+7𝑐
  • C𝑎+4𝑏+14𝑐
  • D(𝑎+4𝑏+7𝑐)
  • E𝑎+4𝑏+49𝑐

Q25:

Expand and simplify (3𝑥+𝑦)12𝑥𝑦, and then factorize the result completely.

  • A(3𝑥+𝑦)
  • B(3𝑥+1)
  • C(3𝑥𝑦)
  • D(3𝑥1)

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