Factorising the difference of two squares
Some quadratic expressions have only a term in x2 and a number such as x2 - 25.
These quadratic expressions have no x term.
Using our method to factorise quadratics means we look for two numbers that multiply to make -25 and add to make 0.
The only factor pair that will work are 5 and -5. So:
(x + 5)(x – 5) = x² - 25
Not all quadratic expressions without an x term can be factorised.
Examples
| These will factorise | These will not factorise |
|---|---|
| x2 - 36 = (x + 6)(x – 6) | x2 - 32 |
| x2 - 100 = (x + 10)(x - 10) | x2 + 100 |
| x2 - 49 = (x + 7)(x – 7) | x2 + 49 |
| x2 - 1 = (x + 1)(x – 1) | x2 - 3 |
In all the examples that will factorise, you have x2 minus a square number.
Factorising these expressions is called the difference of two squares.
Now try the following questions.
- Question
Factorise: x2 - 4
- Answer
x2 - 4 = (x + 2)(x – 2)
- Question
Factorise: x2 - 81
- Answer
x2 - 81 = (x + 9)(x – 9)
- Question
Factorise: x2 - 9
- Answer
x2 - 9 = (x + 3)(x – 3)
Now try a Test Bite
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