Factor 4x^2-7xy-15y^2

$4 x^{2} - 7 x y - 15 y^{2}$

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 $b = - 7$ .

Reorder terms.

$4 x^{2} - 15 y^{2} - 7 x y$

Reorder $- 15 y^{2}$ and $- 7 x y$ .

$4 x^{2} - 7 x y - 15 y^{2}$

Factor $- 7$ out of $- 7 x y$ .

$4 x^{2} - 7 (x y) - 15 y^{2}$

Rewrite $- 7$ as $5$ plus $- 12$

$4 x^{2} + (5 - 12) (x y) - 15 y^{2}$

Apply the distributive property.

$4 x^{2} + 5 (x y) - 12 (x y) - 15 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} + 5 x y - 12 (x y) - 15 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} + 5 x y - 12 x y - 15 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} + 5 x y) - 12 x y - 15 y^{2}$

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

$x (4 x + 5 y) - 3 y (4 x + 5 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 5 y$ .

$(4 x + 5 y) (x - 3 y)$

Factor 4x^2-7xy-15y^2

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