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

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

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Answer 1 · 2016-01-28T23:35:52

$y = x^{3} - 5 x^{2} + 13 x + 4$ $y=x^3-5x^2+13x+4$

Explanation:

Expand each polynomial through distribution.

$y = (x^{2} + 2 x + 2 x + 4) + x (x^{2} - 3 x - 3 x + 9)$ $y=(x^2+2x+2x+4)+x(x^2-3x-3x+9)$

$y = (x^{2} + 4 x + 4) + x (x^{2} - 6 x + 9)$ $y=(x^2+4x+4)+x(x^2-6x+9)$

$y = x^{2} + 4 x + 4 + x^{3} - 6 x^{2} + 9 x$ $y=x^2+4x+4+x^3-6x^2+9x$

$y = x^{3} + (x^{2} - 6 x^{2}) + (4 x + 9 x) + 4$ $y=x^3+(x^2-6x^2)+(4x+9x)+4$

$y = x^{3} - 5 x^{2} + 13 x + 4$ $y=x^3-5x^2+13x+4$

This is in standard form since the terms' exponents are listed in descending order.

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

1 Answer

Explanation:

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