2. Common Factor and Difference of Squares
Factoring means writing an expression as the product of its simplest factors.
Example 1: Factoring a number
`14 = 7 × 2`
[`7` and `2` are the simplest factors of `14`. We can't break it down any more than this.]
Example 2: Factoring an algebraic expression
3x + 15 = 3(x + 5)
This means that the factors of 3x + 15 are
(x + 5)
To be able to factor successfully, we need to recognise the formulas from Section 1. So it's a good idea to learn those formulas well!
Factoring Difference of Two Squares
To factor the difference of 2 squares, we just apply the formula given in Section 1 - Special Products in reverse. That is:
x2 − y2 = (x + y)(x − y)
Example 3: Factoring difference of 2 squares
Factor 36s2 − 121t2
Factor the following:
(1) 18p3 − 3p2
(2) 5a + 10ax − 5ay + 20az
(3) 36a2b 2 − 169c2
(4) (a − b)2 − 1
(5) y4 − 81
(6) r2 − s2 + 2st − t2
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