Question

How do you multiply `(- 2x + 1) ( 2x + 1)`?

Answer 1

`-4x^2+1`

`= 1-4x^2`

Explanation:

There are two approaches we can use.

• multiply the brackets using the `F O I L` method
• consider the brackets as the factors of difference of squares

`F O I L` method first: multiply the

`F` First terms `" "-2x xx 2x = -4x^2`
`O` Outer terms `" "-2x xx 1 = -2x`
`I` Inner terms `" "1 xx 2x = 2x`
`L` Last terms `" "1xx1 = 1`

This gives: `-4x^2 -2x+2x+1 = -4x^2 +1`

Difference of squares method

Note the identity: `" "color(blue)(a^2 -b^2 = (a+b)(a-b))`

If we rewrite the brackets as `(1+2x)(1-2x)` we can see that this is the same form as given in the identity.

Therefore `(1+2x)(1-2x) = 1^2 -(2x)^2`

`= 1-4x^2`