Question

How do you factor `25x^2-81`?

Answer 1

The answer is: `x = 9/5`

You first move the `-81` to the other side of the "equal" sign, it'll become positive instead of negative.

`25x^2 = 81`

We then get the square root of both sides of the equation.

`sqrt(25x^2) = sqrt81`

The square roots are:
`25 = 5 xx 5`
`x^2 = x xx x`
`81 = 9 xx 9`

Applying this to our equation makes it like this.

`5x = 9`

We divide both sides by 5

`(5x)/5 = 9/5`

This cancels both 5 on the `x` side.

`(cancel(5)x)/(cancel(5)) = 9/5`

And we reach our answer:

`x = 9/5`

Answer 2

When you see the numbers 25 and 81, you should realise that we will most probably be using the Sum or Difference of Squares Identities.

As there is a negative sign, we will use the Difference of Squares Identity

It says `color(blue)(a^2 - b^2 = (a+b)(a-b)`

We can write the expression as`(5x)^2 - 9^2`

`=color(green)( (5x+9)(5x - 9)` is the factorised form