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

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

Q1:

For which values of π‘˜ is 16π‘₯+π‘˜π‘₯+81 a perfect square?

  • A13,βˆ’13
  • B72,βˆ’72
  • C36,βˆ’36
  • D26,βˆ’26

Q2:

Which of the following is a perfect square?

  • Aπ‘₯+81
  • Bπ‘₯βˆ’18π‘₯βˆ’81
  • Cπ‘₯βˆ’81
  • Dπ‘₯βˆ’9π‘₯+81
  • Eπ‘₯βˆ’18π‘₯+81

Q3:

Complete the quadratic expression 9π‘₯+144 to make a perfect square.

  • A+72π‘₯οŠͺ
  • B+72π‘₯βˆ’72π‘₯οŠͺοŠͺor
  • C+72π‘₯βˆ’72π‘₯or
  • D+30π‘₯
  • E+36π‘₯βˆ’36π‘₯or

Q4:

Factorize fully π‘₯βˆ’10π‘₯𝑦+25π‘¦οŠ¨οŠ¨.

  • A(βˆ’5π‘₯+𝑦)
  • B(1βˆ’5π‘₯𝑦)
  • C(1+5π‘₯𝑦)
  • D(π‘₯βˆ’5𝑦)
  • E(π‘₯+5𝑦)

Q5:

Factorize fully 81π‘š+18π‘š+1.

  • A(9π‘š+1)(9π‘šβˆ’1)
  • B(π‘šβˆ’9)
  • C(9π‘š+1)
  • D(9π‘š+1)(π‘š+9)
  • E(π‘š+9)

Q6:

Factorize fully 64𝑦π‘₯βˆ’64𝑦π‘₯+16π‘¦οŠ¨.

  • A16(8π‘₯+4)(8π‘₯βˆ’4)
  • B16𝑦(2π‘₯+1)
  • C16𝑦(8βˆ’4π‘₯)
  • D16π‘₯(8βˆ’4𝑦)
  • E16𝑦(2π‘₯βˆ’1)

Q7:

Factorize fully 24π‘₯𝑦+3π‘₯+48π‘¦οŠ¨οŠͺ.

  • A3(π‘₯+4𝑦)
  • B(π‘₯+𝑦)
  • C3(4π‘₯+𝑦)
  • D(π‘₯+4𝑦+3)
  • E(4π‘₯+𝑦)

Q8:

By factorizing or otherwise, evaluate (10.1)βˆ’4.2Γ—10.1+(2.1).

Q9:

By factorizing or otherwise, evaluate (97)+6Γ—97+9.

Q10:

Given that π‘₯+2π‘₯𝑦+𝑦=81, what are the possible values of π‘₯+𝑦?

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

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