Week 10 – Factoring Difference of Squares

A difference of squares if a factorization of (a – b)(a + b)

(a – b)(a + b) = $a^2$ + ab – ba – $b^2$

= $a^2$ – $b^2$

The middle two terms cancel out and you are left with a subtraction of the two terms squared, or a difference of squares.

So, we can apply this distributive property when factoring anything with the same terms but with different signs ( – and + )

Example

(10x – yz)(10x + yz)

Since this follows the rules, we can go straight to

$100x^2$ – $y^2z^2$

We can also work backwards with this factorization.

If we have something such as $144p^2q^2$ – 4

We know that all those terms are squares.

The first step is to determine if there is a common factor that can be removed. In this case, that common factor is 4.

4( $36p^2q^2$ – 1)

Now, we are still left with a difference of squares that we can factor.

4(6pq + 1)(6pq – 1)

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