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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