Factor 15x^2+16xy+4y^2

$15 x^{2} + 16 x y + 4 y^{2}$

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 $a \cdot c = 15 \cdot 4 = 60$ and whose sum is $b = 16$ .

Reorder terms.

$15 x^{2} + 4 y^{2} + 16 x y$

Reorder $4 y^{2}$ and $16 x y$ .

$15 x^{2} + 16 x y + 4 y^{2}$

Factor $16$ out of $16 x y$ .

$15 x^{2} + 16 (x y) + 4 y^{2}$

Rewrite $16$ as $6$ plus $10$

$15 x^{2} + (6 + 10) (x y) + 4 y^{2}$

Apply the distributive property.

$15 x^{2} + 6 (x y) + 10 (x y) + 4 y^{2}$

Remove unnecessary parentheses.

$15 x^{2} + 6 x y + 10 (x y) + 4 y^{2}$

Remove unnecessary parentheses.

$15 x^{2} + 6 x y + 10 x y + 4 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} + 6 x y) + 10 x y + 4 y^{2}$

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

$3 x (5 x + 2 y) + 2 y (5 x + 2 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 2 y$ .

$(5 x + 2 y) (3 x + 2 y)$

Factor 15x^2+16xy+4y^2

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