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

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

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Answer 1 · 2016-06-30T05:56:13

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

Explanation:

In $y = {(x - 3)}^{3}$ $y=(x-3)^3$ , the RHS is a polynomial of degree $3$ $3$ in $x$ $x$ .

The standard form of a polynomial in degree $3$ $3$ is $a x^{3} + b x^{2} + c x + d$ $ax^3+bx^2+cx+d$ , so we should expend ${(x - 3)}^{3}$ $(x-3)^3$ by multiplying.

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

= $(x - 3) (x (x - 3) - 3 (x - 3))$ $(x-3)(x(x-3)-3(x-3))$

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

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

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

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

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

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

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Explanation:

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