Factor 3x^2+14xy+15y^2

$3 x^{2} + 14 x y + 15 y^{2}$

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 $a \cdot c = 3 \cdot 15 = 45$ and whose sum is $b = 14$ .

Reorder terms.

$3 x^{2} + 15 y^{2} + 14 x y$

Reorder $15 y^{2}$ and $14 x y$ .

$3 x^{2} + 14 x y + 15 y^{2}$

Factor $14$ out of $14 x y$ .

$3 x^{2} + 14 (x y) + 15 y^{2}$

Rewrite $14$ as $5$ plus $9$

$3 x^{2} + (5 + 9) (x y) + 15 y^{2}$

Apply the distributive property.

$3 x^{2} + 5 (x y) + 9 (x y) + 15 y^{2}$

Remove unnecessary parentheses.

$3 x^{2} + 5 x y + 9 (x y) + 15 y^{2}$

Remove unnecessary parentheses.

$3 x^{2} + 5 x y + 9 x y + 15 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} + 5 x y) + 9 x y + 15 y^{2}$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + 5 y$ .

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

Factor 3x^2+14xy+15y^2

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