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

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Answer 1 · 2016-01-12T10:53:30

$x^{3} - 10 x^{2} + 21 x - 36$ $x^3 - 10x^2 + 21x - 36$

To obtain standard form require to expand brackets and collect like terms.

${(x - 3)}^{3} - {(x + 3)}^{2}$ $(x - 3 )^3 - (x + 3 )^2$ can be rewritten as follows :

${(x - 3)}^{2} (x - 3) - (x + 3) (x + 3)$ $(x - 3 )^2(x - 3 ) - (x + 3 )(x + 3 )$

expanding ${(x - 3)}^{2} = (x - 3) (x - 3) = x^{2} - 6 x + 9$ $(x - 3 )^2 = (x- 3 )(x - 3 ) = x^2 - 6x + 9$

now becomes ;

$(x^{2} - 6 x + 9) (x - 3) - (x + 3) (x + 3)$ $(x^2 - 6x +9 )(x - 3 ) - (x + 3 )(x + 3 )$

expanding both pairs of brackets :

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

now rewriting with no brackets :

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

Finally collect like terms and write expression in descending order ie. term with highest power → term with lowest power (usually constant term.

$\Rightarrow {(x - 3)}^{3} - {(x + 3)}^{2} = x^{3} - 10 x^{2} + 21 x - 36$ $rArr (x - 3 )^3 - (x + 3 )^2 = x^3 - 10x^2 + 21x - 36$

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