Question

What is the standard form of # y= (x+3)(x-3)^2 #?

Answer 1

`y=x^3-3x^2-9x+27`

Explanation:

Breaking it down into parts.

`color(brown)("Step 1"->)` consider `(x-3)^2`

This is `color(magenta)((x-3))color(blue)((x-3))`

This gives;`color(magenta)(" "xcolor(blue)((x-3)) -3color(blue)((x-3))`

`x^2-3x-3x+9" "=" "x^2-6x+9`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Step 2"->)` Now we have `color(magenta)((x+3))color(blue)((x^2-6x+9))`

This is `color(blue)(x^2color(magenta)((x+3))-6xcolor(magenta)((x+3))+9color(magenta)((x+3)))`

`x^3+3x^2-6x^2-18x+9x+27`

`y=x^3-3x^2-9x+27`