Pre-Algebra Examples

$x^{2} + 2 x y - 80 y^{2}$

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 $a \cdot c = 1 \cdot - 80 = - 80$ and whose sum is $b = 2$ .

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Step 1.1

Reorder terms.

$x^{2} - 80 y^{2} + 2 x y$

Step 1.2

Reorder $- 80 y^{2}$ and $2 x y$ .

$x^{2} + 2 x y - 80 y^{2}$

Step 1.3

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

$x^{2} + 2 (x y) - 80 y^{2}$

Step 1.4

Rewrite $2$ as $- 8$ plus $10$

$x^{2} + (- 8 + 10) (x y) - 80 y^{2}$

Step 1.5

Apply the distributive property.

$x^{2} - 8 (x y) + 10 (x y) - 80 y^{2}$

Step 1.6

Remove unnecessary parentheses.

$x^{2} - 8 x y + 10 (x y) - 80 y^{2}$

Step 1.7

Remove unnecessary parentheses.

$x^{2} - 8 x y + 10 x y - 80 y^{2}$

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.

$(x^{2} - 8 x y) + 10 x y - 80 y^{2}$

Step 2.2

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

$x (x - 8 y) + 10 y (x - 8 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x - 8 y$ .

$(x - 8 y) (x + 10 y)$