Question

How do you factor `x^2-9`?

Answer 1

`(x-3)(x+3)`

Explanation:

`x^2-9" is a "color(blue)"difference of squares"`

`"and in general factorises as"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"here "a=x" and "b=3`

`rArrx^2-9=(x-3)(x+3)`

Answer 2

See a solution process below:

Explanation:

This is a special case of the quadratic:

`color(red)(x)^2 - color(blue)(y)^2 = (color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y))`

`(x^2 - 9 =>`

`color(red)(x)^2 - color(blue)(3)^2 =>`

`(color(red)(x) + color(blue)(3))(color(red)(x) - color(blue)(3))`