Factor 4x^2-4xy-15y^2

$4 x^{2} - 4 x y - 15 y^{2}$

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

Reorder terms.

$4 x^{2} - 15 y^{2} - 4 x y$

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

$4 x^{2} - 4 x y - 15 y^{2}$

Factor $- 4$ out of $- 4 x y$ .

$4 x^{2} - 4 (x y) - 15 y^{2}$

Rewrite $- 4$ as $6$ plus $- 10$

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

Apply the distributive property.

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x + 3 y$ .

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

Factor 4x^2-4xy-15y^2

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