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

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

Q1:

Factor the expression π‘₯βˆ’49.

  • A(2π‘₯+7)
  • B(π‘₯βˆ’7)
  • C(π‘₯+7)(π‘₯βˆ’7)
  • D(π‘₯+49)(π‘₯βˆ’49)
  • E(2π‘₯βˆ’7)

Q2:

Factorize fully 100π‘₯βˆ’121π‘¦οŠ¨οŠ¨.

  • A(11π‘₯βˆ’10𝑦)
  • B(11π‘₯+10𝑦)(11π‘₯βˆ’10𝑦)
  • C21(π‘₯+𝑦)(π‘₯βˆ’π‘¦)
  • D(10π‘₯βˆ’11𝑦)
  • E(10π‘₯+11𝑦)(10π‘₯βˆ’11𝑦)

Q3:

Factorize fully 64π‘₯βˆ’81.

  • A(9π‘₯+8)(9π‘₯βˆ’8)
  • B(π‘₯βˆ’72)
  • C(8π‘₯+9)(8π‘₯βˆ’9)
  • D(π‘₯+72)(π‘₯βˆ’72)
  • E(8π‘₯βˆ’9)

Q4:

Factorize fully 9π‘šβˆ’64𝑛οŠͺοŠͺ.

  • A11ο€Ήπ‘š+π‘›ο…ο€Ήπ‘šβˆ’π‘›ο…οŠ¨οŠ¨οŠ¨οŠ¨
  • Bο€Ή8π‘š+3𝑛8π‘šβˆ’3π‘›ο…οŠ¨οŠ¨οŠ¨οŠ¨
  • Cο€Ή3π‘š+8𝑛3π‘šβˆ’8π‘›ο…οŠ¨οŠ¨οŠ¨οŠ¨
  • Dο€Ή8π‘šβˆ’3π‘›ο…οŠ¨οŠ¨οŠ¨
  • E(3π‘šβˆ’8𝑛)οŠͺ

Q5:

Factorize fully 49π‘Žβˆ’64π‘π‘οŠ¨οŠ¨οŠͺ.

  • Aο€Ή7π‘Ž+8𝑏𝑐7π‘Žβˆ’8π‘π‘ο…οŠ¨οŠ¨
  • Bο€Ή7π‘Žβˆ’8π‘π‘ο…οŠ¨οŠ¨
  • C(7π‘Ž+8𝑏𝑐)(7π‘Žβˆ’8𝑏𝑐)
  • D(7π‘Žβˆ’8𝑏𝑐)
  • Eο€Ή49π‘Ž+64𝑏𝑐49π‘Žβˆ’64π‘π‘ο…οŠ¨οŠ¨

Q6:

Factorize fully (π‘₯+4𝑦+3)βˆ’(π‘₯βˆ’4π‘¦βˆ’3).

  • A4𝑦(4π‘₯+3)
  • B(4π‘₯βˆ’3𝑦)
  • C4(4𝑦+3π‘₯)
  • D4π‘₯(4𝑦+3)
  • E(4π‘₯π‘¦βˆ’3)

Q7:

If π‘₯𝑦=8, what is the value of (π‘₯+3𝑦)βˆ’(π‘₯βˆ’3𝑦)?

Q8:

By factorizing or otherwise, evaluate (77)βˆ’(23).

Q9:

By factoring or otherwise, evaluate 5Γ—(8.85)βˆ’5Γ—(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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