Factor 8x^2-2xy-1y^2

$8 x^{2} - 2 x y - 1 y^{2}$

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 $a \cdot c = 8 \cdot - 1 = - 8$ and whose sum is $b = - 2$ .

Reorder terms.

$8 x^{2} - 1 y^{2} - 2 x y$

Reorder $- 1 y^{2}$ and $- 2 x y$ .

$8 x^{2} - 2 x y - 1 y^{2}$

Factor $- 2$ out of $- 2 x y$ .

$8 x^{2} - 2 (x y) - 1 y^{2}$

Rewrite $- 2$ as $2$ plus $- 4$

$8 x^{2} + (2 - 4) (x y) - 1 y^{2}$

Apply the distributive property.

$8 x^{2} + 2 (x y) - 4 (x y) - 1 y^{2}$

Remove unnecessary parentheses.

$8 x^{2} + 2 x y - 4 (x y) - 1 y^{2}$

Remove unnecessary parentheses.

$8 x^{2} + 2 x y - 4 x y - 1 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} + 2 x y) - 4 x y - 1 y^{2}$

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

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

Step 3

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

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

Factor 8x^2-2xy-1y^2

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