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

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Answer 1 · 2015-12-02T20:55:47

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

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

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

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

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

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

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