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

May 3, 2015

The answer is: $x = \frac{9}{5}$

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

$25 {x}^{2} = 81$

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

$\sqrt{25 {x}^{2}} = \sqrt{81}$

The square roots are:
$25 = 5 \times 5$
${x}^{2} = x \times x$
$81 = 9 \times 9$

Applying this to our equation makes it like this.

$5 x = 9$

We divide both sides by 5

$\frac{5 x}{5} = \frac{9}{5}$

This cancels both 5 on the $x$ side.

$\frac{\cancel{5} x}{\cancel{5}} = \frac{9}{5}$

$x = \frac{9}{5}$

May 3, 2015

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${\left(5 x\right)}^{2} - {9}^{2}$

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