Factor 10x^2+31xy-14y^2

$10 x^{2} + 31 x y - 14 y^{2}$

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 $a \cdot c = 10 \cdot - 14 = - 140$ and whose sum is $b = 31$ .

Reorder terms.

$10 x^{2} - 14 y^{2} + 31 x y$

Reorder $- 14 y^{2}$ and $31 x y$ .

$10 x^{2} + 31 x y - 14 y^{2}$

Factor $31$ out of $31 x y$ .

$10 x^{2} + 31 (x y) - 14 y^{2}$

Rewrite $31$ as $- 4$ plus $35$

$10 x^{2} + (- 4 + 35) (x y) - 14 y^{2}$

Apply the distributive property.

$10 x^{2} - 4 (x y) + 35 (x y) - 14 y^{2}$

Remove unnecessary parentheses.

$10 x^{2} - 4 x y + 35 (x y) - 14 y^{2}$

Remove unnecessary parentheses.

$10 x^{2} - 4 x y + 35 x y - 14 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 x^{2} - 4 x y) + 35 x y - 14 y^{2}$

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

$2 x (5 x - 2 y) + 7 y (5 x - 2 y)$

Step 3

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

$(5 x - 2 y) (2 x + 7 y)$

Factor 10x^2+31xy-14y^2

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