Year 9

# Difference of two squares

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## Lesson details

### Key learning points

- In this lesson, we will learn about the difference of two squares. We will investigate the pattern of results when considering multiplying out brackets of the general form (x+a)(x-a).

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### 6 Questions

Q1.

Choose the word which best fills the gap: When we ________ double brackets every term in the first bracket must be multiplied by every term in the second bracket.

divide

express

factorise

Q2.

Expand and simplify (x+2)(x+5)

18x²

x² + 10

x² + 17x

Q3.

Expand and simplify (x+2)(x-5)

x² - 10

x² - 7x + 10

x² + 3x + 10

Q4.

Expand and simplify 2(x+3)-2(x+5)

-4x

2x² - 6x + 20

None of the answers above.

Q5.

A rectangle has side lengths (x+4) and (x-3). Match the expression that would represent it's area.

20x²

x² - x + 12

x² + 7x - 12

Q6.

Yasmin expanded (a + x + 3)(x + 2). Below are her workings out. Which expression matches the area of the rectangle she has created?

13ax²

ax² + 7ax + 6

x² + a + 5x + 8a

### 6 Questions

Q1.

Which expression is equivalent to a² - b² ?

(a - b)(a - b)

2ab

ab

Q2.

Match the expression equivalent to (x+4)(x-4).

x² - 16x

x² - 4

x² - 8x + 16

x² + 4²

Q3.

Match the expression equivalent to (x+9)(x-3).

x² - 3²

x² - 6²

x² + 3x - 27

Q4.

Which calculation would work out 64² - 4² ?

(8 x 2)²

60 x 60

72 x 6

Q5.

Match the expression equivalent to (x+25)-(x-25).

x² - 25

x² - 25²

x² + 5²

Q6.

Match the expression equivalent to (73+x)(73-x).

73 - x²

73 + x²

x² - 73

x² - 73²