Factor x^2-2xy-48y^2

$x^{2} - 2 x y - 48 y^{2}$

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 $a \cdot c = 1 \cdot - 48 = - 48$ and whose sum is $b = - 2$ .

Reorder terms.

$x^{2} - 48 y^{2} - 2 x y$

Reorder $- 48 y^{2}$ and $- 2 x y$ .

$x^{2} - 2 x y - 48 y^{2}$

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

$x^{2} - 2 (x y) - 48 y^{2}$

Rewrite $- 2$ as $6$ plus $- 8$

$x^{2} + (6 - 8) (x y) - 48 y^{2}$

Apply the distributive property.

$x^{2} + 6 (x y) - 8 (x y) - 48 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 6 x y - 8 (x y) - 48 y^{2}$

Remove unnecessary parentheses.

$x^{2} + 6 x y - 8 x y - 48 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} + 6 x y) - 8 x y - 48 y^{2}$

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

$x (x + 6 y) - 8 y (x + 6 y)$

Step 3

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

$(x + 6 y) (x - 8 y)$

Factor x^2-2xy-48y^2

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