Question

The standard form of `y = (2x +3)^3 ­- (4x-2)^2`?

Answer 1

`:.color(blue)(y=8x^3+20x^2+70x+23`

Explanation:

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

First simplify `(2x+3)^3`

`color(white)(aaaaaaaaaaaaa)` `2x+3`

`color(white)(aaaaaaaaaaa)` `underline( xx 2x+3)`
`color(white)(aaaaaaaaaaaaa)` `4x^2+6x`
`color(white)(aaaaaaaaaaaaaaaaaaa)` `6x+9`
`color(white)(aaaaaaaaaaaaa)` `overline(4x^2+12x+9)`
`color(white)(aaaaaaaaaaa)` `xx 2x+3`
`color(white)(aaaaaaaaaaaaa)` `overline(8x^3+24x^2+18x)`
`color(white)(aaaaaaaaaaaaaaaaaa)` `12x^2+36x+27`
`color(white)(aaaaaaaaaaaaa)` `overline(color(purple)(8x^3+36x^2+54x+27)`

Then simplify `color(green)((4x-2)^2`

`color(green)(=(4x-2)(4x-2))`

`:.color(green)((4x-2)^2=16x^2-16x+4`

`color(purple)((2x+3)^3=8x^3+36x^2+54x+27`

`:.y=8x^3+36x^2+54x+27-(16x^2-16x+4)`

`:.color(orange)(y=8x^3+36x^2+54x+27-16x^2+16x-4)`

`:.color(blue)(y=8x^3+20x^2+70x+23`