Factor 4x^2+xy-14y^2

$4 x^{2} + x y - 14 y^{2}$

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 $a \cdot c = 4 \cdot - 14 = - 56$ and whose sum is $b = 1$ .

Reorder terms.

$4 x^{2} - 14 y^{2} + x y$

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

$4 x^{2} + x y - 14 y^{2}$

Factor $1$ out of $x y$ .

$4 x^{2} + 1 (x y) - 14 y^{2}$

Rewrite $1$ as $- 7$ plus $8$

$4 x^{2} + (- 7 + 8) (x y) - 14 y^{2}$

Apply the distributive property.

$4 x^{2} - 7 (x y) + 8 (x y) - 14 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} - 7 x y + 8 (x y) - 14 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} - 7 x y + 8 x y - 14 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 7 x y) + 8 x y - 14 y^{2}$

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

$x (4 x - 7 y) + 2 y (4 x - 7 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 7 y$ .

$(4 x - 7 y) (x + 2 y)$

Factor 4x^2+xy-14y^2

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