Worksheet: Factoring Perfect-Square Trinomials

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:

Complete the expression 16π‘₯+𝑦οŠͺ to make a perfect square.

  • A+8π‘₯π‘¦βˆ’8π‘₯π‘¦οŠ¨οŠ¨or
  • B+10π‘₯π‘¦βˆ’10π‘₯π‘¦οŠ¨οŠ¨or
  • C+4π‘₯π‘¦βˆ’4π‘₯π‘¦οŠ¨οŠ¨or
  • D+8π‘₯π‘¦βˆ’8π‘₯𝑦or

Q3:

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

Q4:

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

Q5:

If 9𝑦+30𝑦+π‘οŠ¨ is a perfect square, what is the value of 𝑏?

Q6:

Complete the expression βˆ’60π‘₯+25 to make a perfect square.

  • Aβˆ’36π‘₯οŠͺ
  • Bβˆ’12π‘₯οŠͺ
  • C12π‘₯οŠͺ
  • D36π‘₯οŠͺ
  • E6π‘₯

Q7:

Complete the expression 425π‘Ž+19π‘οŠ¨οŠ¨ to make a perfect square.

  • AΒ±415π‘Žπ‘
  • B+45π‘Žπ‘
  • C+25π‘Žπ‘
  • DΒ±215π‘Žπ‘
  • EΒ±415π‘Žπ‘οŠ¨

Q8:

If π‘˜π‘¦βˆ’24𝑦+9 is a perfect square, what is the value of π‘˜?

Q9:

Factorize fully 9π‘₯+36π‘₯𝑦+36𝑦οŠͺοŠͺ.

  • A9(2π‘₯+𝑦)
  • B9(π‘₯+2𝑦)
  • C(π‘₯+2𝑦)
  • D9(𝑦+2π‘₯)
  • E9(π‘₯+2𝑦)

Q10:

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)

Q11:

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

Q12:

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)

Q13:

Factorize fully 4(π‘₯βˆ’7)βˆ’16(π‘₯βˆ’7)(π‘¦βˆ’6)+16(π‘¦βˆ’6).

  • A(2π‘₯βˆ’4π‘¦βˆ’38)
  • B(2π‘₯βˆ’4𝑦)
  • C(2π‘₯βˆ’4𝑦+10)
  • Dο€Ή2π‘₯βˆ’4𝑦+10ο…οŠ¨οŠ¨οŠ¨
  • E(π‘₯+π‘¦βˆ’2)

Q14:

Complete the expression 81π‘₯+90π‘₯𝑦+β‹―οŠ¨ to make a perfect square.

  • A25π‘¦οŠ¨
  • B20π‘¦οŠ¨
  • Cβˆ’25𝑦
  • D9𝑦
  • E25𝑦

Q15:

Factorize fully 4981π‘₯+89π‘₯+1649.

  • Aο€Ό79π‘₯βˆ’27
  • Bο€Ό79π‘₯+47
  • Cο€Ό79π‘₯+47
  • Dο€Ό79π‘₯+27
  • Eο€Ό79π‘₯βˆ’47

Q16:

Expand and simplify 5π‘₯(5π‘₯+18𝑦)+81π‘¦οŠ¨, then factorize the result.

  • A(5π‘₯βˆ’9𝑦)
  • B(5π‘₯+9)
  • C(5π‘₯+8)
  • D(5π‘₯+8𝑦)
  • E(5π‘₯+9𝑦)

Q17:

By factorizing or otherwise, evaluate (97)+6Γ—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 481π‘₯βˆ’43π‘₯+9.

  • Aο€Ό29π‘₯+3οˆο€Ό29π‘₯βˆ’3
  • Bο€Ό29π‘₯βˆ’3
  • Cο€Ό3π‘₯βˆ’29
  • D(9π‘₯βˆ’3)
  • Eο€Ό3π‘₯+29οˆο€Ό3π‘₯βˆ’29

Q20:

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

Q21:

Factorize fully π‘Ž+6π‘Ž+9π‘ŽοŠͺ.

  • A(π‘Ž+3)
  • Bπ‘Ž(π‘Ž+3)
  • Cπ‘Ž(3π‘Ž+1)
  • Dπ‘Ž(3π‘Ž+1)(3π‘Žβˆ’1)
  • Eπ‘Ž(3π‘Ž+1)

Q22:

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)

Q23:

Write all possible expressions for π‘˜ such that π‘₯+π‘˜+4π‘¦οŠ¨οŠ¨ is a perfect square.

  • A4,βˆ’4
  • B2π‘₯𝑦,βˆ’2π‘₯𝑦
  • C4π‘₯𝑦,βˆ’4π‘₯𝑦
  • D6π‘₯𝑦,βˆ’6π‘₯𝑦

Q24:

Factorize fully (π‘Ž+4𝑏)+14𝑐(π‘Ž+4𝑏)+49π‘οŠ¨οŠ¨οŠͺ.

  • Aο€Ήπ‘Ž+4π‘βˆ’7π‘ο…οŠ¨οŠ¨
  • Bο€Ήπ‘Ž+4𝑏+7π‘ο…οŠ¨οŠ¨
  • Cο€Ήπ‘Ž+4𝑏+14π‘ο…οŠ¨οŠ¨
  • D(π‘Ž+4𝑏+7𝑐)
  • Eο€Ήπ‘Ž+4𝑏+49π‘ο…οŠ¨οŠ¨

Q25:

Expand and simplify (3π‘₯+𝑦)βˆ’12π‘₯π‘¦οŠ¨, and then factorize the result completely.

  • A(3π‘₯+𝑦)
  • B(3π‘₯+1)
  • C(3π‘₯βˆ’π‘¦)
  • D(3π‘₯βˆ’1)

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