Factor 6x^2+41xy-7y^2

$6 x^{2} + 41 x y - 7 y^{2}$

Step 1

Factor by grouping.

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 $a \cdot c = 6 \cdot - 7 = - 42$ and whose sum is $b = 41$ .

Reorder terms.

$6 x^{2} - 7 y^{2} + 41 x y$

Reorder $- 7 y^{2}$ and $41 x y$ .

$6 x^{2} + 41 x y - 7 y^{2}$

Factor $41$ out of $41 x y$ .

$6 x^{2} + 41 (x y) - 7 y^{2}$

Rewrite $41$ as $- 1$ plus $42$

$6 x^{2} + (- 1 + 42) (x y) - 7 y^{2}$

Apply the distributive property.

$6 x^{2} - 1 (x y) + 42 (x y) - 7 y^{2}$

Remove unnecessary parentheses.

$6 x^{2} - 1 x y + 42 (x y) - 7 y^{2}$

Remove unnecessary parentheses.

$6 x^{2} - 1 x y + 42 x y - 7 y^{2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 x^{2} - 1 x y) + 42 x y - 7 y^{2}$

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

$x (6 x - 1 y) + 7 y (6 x - y)$

Factor the polynomial by factoring out the greatest common factor, $6 x - 1 y$ .

$(6 x - 1 y) (x + 7 y)$

Step 2

Rewrite $- 1 y$ as $- y$ .

$(6 x - y) (x + 7 y)$

Factor 6x^2+41xy-7y^2

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