Question

What is the standard form of `y= (2x+4)(-x+5)(-x+1)`?

Answer 1

`y = -2x^3-8x^2-14x+1`

Explanation:

`y = (-2x^2+10x-4x+20)(-x+1)`
`y = (-2x^2+6x+20)(-x+1)`
`y = -2x^3-2x^2-6x^2+6x-20x+1`
`y = -2x^3-8x^2-14x+1`

Always factor the harder one first, otherwise, factor left to right.

Answer 2

`color(blue)(y=2x^3-8x^2-14x+20`

Explanation:

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

`color(white)(aaaaaaaaaaaaa)` `2x+4`
`color(white)(aaaaaaaaaa)` `xx underline(-x+5)`
`color(white)(aaaaaaaaaaa)` `-2x^2-4x`
`color(white)(aaaaaaaaaaaaaaaaa)` `10x+20`
`color(white)(aaaaaaaaaaa)` `overline(-2x^2+6x+20)`
`color(white)(aaaaaaaa)` `xx -x+1`
`color(white)(aaaaaaaaaaaa)` `overline(2x^3-6x^2-20x)`
`color(white)(aaaaaaaaaaaaaaa)` `-2x^2+6x+20`
`color(white)(aaaaaaaa)` `color(blue)(y=overline(2x^3-8x^2-14x+20)`