Algebra Examples

$x^{2} + 3 x y + 2 y^{2}$

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 $a \cdot c = 1 \cdot 2 = 2$ and whose sum is $b = 3$ .

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Step 1.1

Reorder terms.

$x^{2} + 2 y^{2} + 3 x y$

Step 1.2

Reorder $2 y^{2}$ and $3 x y$ .

$x^{2} + 3 x y + 2 y^{2}$

Step 1.3

Factor $3$ out of $3 x y$ .

$x^{2} + 3 (x y) + 2 y^{2}$

Step 1.4

Rewrite $3$ as $1$ plus $2$

$x^{2} + (1 + 2) (x y) + 2 y^{2}$

Step 1.5

Apply the distributive property.

$x^{2} + 1 (x y) + 2 (x y) + 2 y^{2}$

Step 1.6

Multiply $x y$ by $1$ .

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

Step 1.7

Remove unnecessary parentheses.

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

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.

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

Step 2.2

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

$x (x + y) + 2 y (x + y)$

Step 3

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

$(x + y) (x + 2 y)$