Question

How do you solve `x^2 - 16 = 0` by factoring?

Answer 1

The solutions are
`color(blue)(x=-4,x=4`

Explanation:

As per property
`color(blue)(a^2-b^2)=(a+b)(a-b)`

Expressing the given equation in the same manner:

`x^2-16=color(blue)(x^2-4^2`

`x^2-4^2 = color(blue)((x+4)(x-4)`

Now we equate the factors to zero to obtain the solutions

`x+4 =0, color(blue)(x=-4`
`x-4 =0, color(blue)(x=4`