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

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Answer 1 · 2016-03-29T19:05:35

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

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 $color(blue)(x^2color(magenta)((x+3))-6xcolor(magenta)((x+3))+9color(magenta)((x+3)))$

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

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

Tony B

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