Lesson Worksheet: Expanding an Expression to a Difference of Two Squares Mathematics • 9th Grade

In this worksheet, we will practice multiplying the sum of two terms by their difference to get the polynomial known as the difference of two squares.

Q1:

Expand the product (π‘₯+1)(π‘₯βˆ’1).

  • Aπ‘₯+1
  • Bπ‘₯βˆ’2π‘₯βˆ’1
  • Cπ‘₯+2π‘₯βˆ’1
  • Dπ‘₯βˆ’1
  • Eπ‘₯+2π‘₯+1

Q2:

Use the difference of two squares identity to expand (3π‘Ž+7)(3π‘Žβˆ’7).

  • A6π‘Žβˆ’14
  • B9π‘Žβˆ’7
  • C9π‘Žβˆ’49
  • D9π‘Žβˆ’49
  • E3π‘Žβˆ’49

Q3:

If π‘₯βˆ’π‘Ž=(π‘₯+5)(π‘₯βˆ’5), what is the value of π‘Ž?

Q4:

Expand the product (2π‘š+𝑛)(2π‘šβˆ’π‘›).

  • A4π‘š+2π‘šπ‘›+π‘›οŠ¨οŠ¨
  • B4π‘š+2π‘šπ‘›βˆ’π‘›οŠ¨οŠ¨
  • C4π‘šβˆ’2π‘šπ‘›+π‘›οŠ¨οŠ¨
  • D4π‘šβˆ’π‘›οŠ¨οŠ¨
  • E4π‘š+π‘›οŠ¨οŠ¨

Q5:

If π‘₯βˆ’π‘¦=9 and π‘₯+𝑦=10, what is the value of π‘₯βˆ’π‘¦οŠ¨οŠ¨?

Q6:

Complete the following: π‘₯βˆ’=(π‘₯βˆ’5)(π‘₯+5).

Q7:

If π‘₯+𝑦=2 and π‘₯βˆ’π‘¦=6, what is the value of π‘₯βˆ’π‘¦οŠ¨οŠ¨?

Q8:

If π‘₯+π‘™βˆ’25=(π‘₯+5)(π‘₯βˆ’5), what is the value of 𝑙?

Q9:

Given that 𝑛+π‘š=5 and π‘›βˆ’π‘š=45, find π‘›βˆ’π‘š.

Q10:

If π‘šβˆ’π‘›=64 and π‘š+𝑛=4, what is the value of π‘šβˆ’π‘›?

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