How do you factor $y = x^{3} + 9 x^{2} + 27 x + 27$ $y= x^3 + 9x^2 + 27x + 27$ ?

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How do you factor $y = x^{3} + 9 x^{2} + 27 x + 27$ $y= x^3 + 9x^2 + 27x + 27$ ?

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Answer 1 · 2015-12-02T20:55:47

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

Explanation:

Notice that $x^{3}$ $x^3$ is a perfect cube and $27 = 3^{3}$ $27 = 3^3$ is also a perfect cube.

So try ${(x + 3)}^{3}$ $(x+3)^3$ to see if the middle two terms match.

In general ${(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$ $(a+b)^3 = a^3+3a^2b+3ab^2+b^3$ , so:

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

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

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How do you factor $y = x^{3} + 9 x^{2} + 27 x + 27$ $y= x^3 + 9x^2 + 27x + 27$ ?

1 Answer

Explanation:

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How do you factor $y = x^{3} + 9 x^{2} + 27 x + 27$ $y= x^3 + 9x^2 + 27x + 27$ ?