Factor 9x^2+15xy+4y^2

$9 x^{2} + 15 x y + 4 y^{2}$

Step 1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 9 \cdot 4 = 36$ and whose sum is $b = 15$ .

Reorder terms.

$9 x^{2} + 4 y^{2} + 15 x y$

Reorder $4 y^{2}$ and $15 x y$ .

$9 x^{2} + 15 x y + 4 y^{2}$

Factor $15$ out of $15 x y$ .

$9 x^{2} + 15 (x y) + 4 y^{2}$

Rewrite $15$ as $3$ plus $12$

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

Apply the distributive property.

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

Factor out the greatest common factor (GCF) from each group.

$3 x (3 x + y) + 4 y (3 x + y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + y$ .

$(3 x + y) (3 x + 4 y)$

Factor 9x^2+15xy+4y^2

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