## 16 Dec Difference of Two Squares

Difference of Two squares

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Let us start by expanding (x+y)(x-y):

(x+y)(x-y)

= x² -xy +xy -y²

= x² – y²

This means that x² – y² = (x-y)(x+y)

The above expression gives us a method for working out the difference of two squares.

This expression can be written in words as:

<b>The difference of the squares of two quantities is equal to the product of their sum and their difference .</b>

Example 1: Using the difference of two squares, solve 15² – 10²

SOLUTION

Comparing 15² – 10² to

x² – y² = (x-y)(x+y)

It follows that:

15² – 10²

= (15-10)(15+10)

= (5)(25)

= 125

Difference of two squares can also be used to factorise expressions

Example 3: Factorise the following:

1) y² – 16

2) 81 – 4b²

3). 25b² – 16c²

SOLUTION

1) y² – 16

Note that 16 is a perfect square and it can be expressed as the power of 4.

Therefore,

y² – 16 = y² – 4²

= (y – 4)(y + 4)

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