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

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

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Answer 1 · 2016-03-29T19:05:35

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

Explanation:

Breaking it down into parts.

$Step 1 \to$ $color(brown)("Step 1"->)$ consider ${(x - 3)}^{2}$ $(x-3)^2$

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

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

$x^{2} - 3 x - 3 x + 9 = x^{2} - 6 x + 9$ $x^2-3x-3x+9" "=" "x^2-6x+9$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Step 2 \to$ $color(brown)("Step 2"->)$ Now we have $(x + 3) (x^{2} - 6 x + 9)$ $color(magenta)((x+3))color(blue)((x^2-6x+9))$

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

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

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

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

1 Answer

Explanation:

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