How do you factor $x^{2} + 6 x y + 9 y^{2}$ $x^2 + 6xy + 9y^2$ ?

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How do you factor $x^{2} + 6 x y + 9 y^{2}$ $x^2 + 6xy + 9y^2$ ?

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Answer 1 · 2015-05-20T14:57:44

You can factor this by grouping.

The coefficients of $x^{2}$ $x^2$ and $y^{2}$ $y^2$ are, respectively, $1$ $1$ and $9$ $9$ , the product of which is $9$ $9$ , which, in turn, can be factored in $(3) (3)$ $(3)(3)$ .

So, we can rewrite our function as

$x^{2} + 3 x y + 9 y^{2} + 3 x y$ $x^2+3xy+9y^2+3xy$

and factor it by two groups of two terms each:

$x (x + 3 y) + 3 y (3 y + x)$ $color(green)(x)(color(blue)(x+3y)) + color(green)(3y)(color(blue)(3y+x))$

We can see that the parenthesis of each term are exactly the same, so we can use them as the common multiple of the whole equation that are multipling the rest:

$(x + 3 y) (x + 3 y)$ $(color(blue)(x+3y))(color(green)(x+3y))$

Done!

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How do you factor $x^{2} + 6 x y + 9 y^{2}$ $x^2 + 6xy + 9y^2$ ?

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