Algebra Examples

$x^{2} + 13 x y + 40 y^{2}$

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 $a \cdot c = 1 \cdot 40 = 40$ and whose sum is $b = 13$ .

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Step 1.1

Reorder terms.

$x^{2} + 40 y^{2} + 13 x y$

Step 1.2

Reorder $40 y^{2}$ and $13 x y$ .

$x^{2} + 13 x y + 40 y^{2}$

Step 1.3

Factor $13$ out of $13 x y$ .

$x^{2} + 13 (x y) + 40 y^{2}$

Step 1.4

Rewrite $13$ as $5$ plus $8$

$x^{2} + (5 + 8) (x y) + 40 y^{2}$

Step 1.5

Apply the distributive property.

$x^{2} + 5 (x y) + 8 (x y) + 40 y^{2}$

Step 1.6

Remove unnecessary parentheses.

$x^{2} + 5 x y + 8 (x y) + 40 y^{2}$

Step 1.7

Remove unnecessary parentheses.

$x^{2} + 5 x y + 8 x y + 40 y^{2}$

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.

$(x^{2} + 5 x y) + 8 x y + 40 y^{2}$

Step 2.2

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

$x (x + 5 y) + 8 y (x + 5 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x + 5 y$ .

$(x + 5 y) (x + 8 y)$