Vocabulary
Algebraic expressions like a² - b² or
x² -4, where both terms are perfect squares, are called the difference
of two squares. |
Expressions like these can always be
factorised.
For example, x ² - 1=( x - 1)( x
+ 1) or a² - 9=(a -3 )(a + 3)
Example: factorise x² - 16
| Step 1: |
Write down some "empty"
brackets |
x² -
16= |
(
)( ) |
| Step 2: |
The first terms in each bracket must both
be x: |
|
(x
)(x ) |
| Step 3:
|
The last terms in each bracket must
multiply to give -16 and be of equal size, ie. 4 and -4 |
|
(x + 4)(x -
4) |
| Step 4: |
Check that you get the correct result when
you multiply out the brackets. |
|
|
|
