Question

How do you write `f(x)=4*(x-3)(x+7)` into standard form?

Answer 1

`f(x) = 4x^2+16x-84`

Explanation:

You can use the FOIL mnemonic to enumerate all of the combinations you need to add together if you find it helpful:

`f(x) = 4*(x-3)(x+7)`

`color(white)(f(x)) = 4(overbrace((x)(x))^"First"+overbrace((x)(7))^"Outside"+overbrace((-3)(x))^"Inside"+overbrace((-3)(7))^"Last")`

`color(white)(f(x)) = 4(x^2+7x-3x-21)`

`color(white)(f(x)) = 4(x^2+4x-21)`

`color(white)(f(x)) = 4x^2+16x-84`