Algebra Examples

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

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

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Step 1.1

Reorder terms.

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

Step 1.2

Reorder $- 8 y^{2}$ and $2 x y$ .

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

Apply the distributive property.

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

Step 1.6

Remove unnecessary parentheses.

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

Step 1.7

Remove unnecessary parentheses.

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

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

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

Step 2.2

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

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

Step 3

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

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