Question

How do you factor `144x²-81`?

Answer 1

This is of the form `a^2-b^2`, since both `144` and `81` are squares

Explanation:

We can even take out `9` and still have squares:
`=9xx16x^2-9xx3^2=9(16x^2-9)`

`=9(4^2xxx^2-3^2)=9((4x)^2-3^2)`

Since `a^2-b^2harr(a+b)(a-b)`:

`=9(4x+3)(4x-3)`

Answer 2

`9(4x-3)(4x+3)`

Explanation:

`9(16x^2-9)`

This can then be simplified to:

`9(4x-3)(4x+3)` using the difference of two squares rule.

Therefore, `x=±3/4`

Or, you could solve for `x` like this:

`144x^2-81`

`144x^2=81`

`x^2=81/144`

`x=±sqrt(81/144)`

`x= 3/4`

`x=-3/4`