Question

What is the standard form of `y= (4x-4)(x^2+5x-5)`?

Answer 1

`y=4x^3+16x^2-40x+20`

Explanation:

For convenience, separate out the scalar factor `4` temporarily while multiplying out, group the terms in descending degree and combine. For illustration I have shown more steps than normal:

`(4x-4)(x^2+5x-5)`

`=4(x-1)(x^2+5x-5)`

`=4(x(x^2+5x-5)-1(x^2+5x-5))`

`=4((x^3+5x^2-5x)-(x^2+5x-5))`

`=4(x^3+5x^2-5x-x^2-5x+5)`

`=4(x^3+(5x^2-x^2)+(-5x-5x)+5)`

`=4(x^3+(5-1)x^2+(-5-5)x+5)`

`=4(x^3+4x^2-10x+5)`

`=4x^3+16x^2-40x+20`

Alternatively, just look at the combinations of terms to give each power of `x` in descending order like this:

`(4x-4)(x^2+5x-5)`

`=4x^3+(20-4)x^2-(20+20)x+20`

`=4x^3+16x^2-40x+20`