How do you factor #12x^2 + 36xy + 27y^2?

Question

3618 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-08T04:04:59

$f (x) = 3 (4 x^{2} + 12 x y + 9 y^{2}) = 3 {(2 x + 3 y)}^{2}$ $f(x) = 3(4x^2 + 12xy + 9y^2) = 3(2x + 3y)^2$

Answer 2 · 2015-06-08T05:31:58

Answer: $12 x^{2} + 36 x y + 27 y^{2} = 3 {(2 x + 3 y)}^{2}$ $12x^2+36xy+27y^2=3(2x+3y)^2$

Problem: Factor $12 x^{2} + 36 x y + 27 y^{2}$ $12x^2+36xy+27y^2$ .

Factor out the GCF $3$ $3$ .

$3 (4 x^{2} + 12 x y + 9 y^{2})$ $3(4x^2+12xy+9y^2)$

$(4 x^{2} + 12 x y + 9 y^{2})$ $(4x^2+12xy+9y^2)$ is a perfect square trinomial with the pattern

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ $(a+b)^2=a^2+2ab+b^2$ .

$a = 2 x$ $a=2x$
$b = 3 y$ $b=3y$

$(4 x^{2} + 12 x y + 9 y^{2}) = {(2 x + 3 y)}^{2}$ $(4x^2+12xy+9y^2)=(2x+3y)^2$

$12 x^{2} + 36 x y + 27 y^{2} = 3 {(2 x + 3 y)}^{2}$ $12x^2+36xy+27y^2=3(2x+3y)^2$