Factor x^2+5x(x+2y)+6(x+2y)^2

$x^{2} + 5 x (x + 2 y) + 6 {(x + 2 y)}^{2}$

Step 1

Factor by grouping.

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 $a \cdot c = 1 \cdot 6 = 6$ and whose sum is $b = 5$ .

Reorder terms.

$x^{2} + 6 {(x + 2 y)}^{2} + 5 x (x + 2 y)$

Reorder $6 {(x + 2 y)}^{2}$ and $5 x (x + 2 y)$ .

$x^{2} + 5 x (x + 2 y) + 6 {(x + 2 y)}^{2}$

Factor $5$ out of $5 x (x + 2 y)$ .

$x^{2} + 5 (x (x + 2 y)) + 6 {(x + 2 y)}^{2}$

Rewrite $5$ as $2$ plus $3$

$x^{2} + (2 + 3) (x (x + 2 y)) + 6 {(x + 2 y)}^{2}$

Apply the distributive property.

$x^{2} + 2 (x (x + 2 y)) + 3 (x (x + 2 y)) + 6 {(x + 2 y)}^{2}$

Remove unnecessary parentheses.

$x^{2} + 2 x (x + 2 y) + 3 (x (x + 2 y)) + 6 {(x + 2 y)}^{2}$

Remove unnecessary parentheses.

$x^{2} + 2 x (x + 2 y) + 3 x (x + 2 y) + 6 {(x + 2 y)}^{2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} + 2 x (x + 2 y)) + 3 x (x + 2 y) + 6 {(x + 2 y)}^{2}$

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

$x (x + 2 (x + 2 y)) + 3 (x + 2 y) (x + 2 (x + 2 y))$

Factor the polynomial by factoring out the greatest common factor, $x + 2 (x + 2 y)$ .

$(x + 2 (x + 2 y)) (x + 3 (x + 2 y))$

Step 2

Apply the distributive property.

$(x + 2 x + 2 (2 y)) (x + 3 (x + 2 y))$

Step 3

Multiply $2$ by $2$ .

$(x + 2 x + 4 y) (x + 3 (x + 2 y))$

Step 4

Add $x$ and $2 x$ .

$(3 x + 4 y) (x + 3 (x + 2 y))$

Step 5

Apply the distributive property.

$(3 x + 4 y) (x + 3 x + 3 (2 y))$

Step 6

Multiply $2$ by $3$ .

$(3 x + 4 y) (x + 3 x + 6 y)$

Step 7

Add $x$ and $3 x$ .

$(3 x + 4 y) (4 x + 6 y)$

Step 8

Factor.

Factor $2$ out of $4 x + 6 y$ .

Factor $2$ out of $4 x$ .

$(3 x + 4 y) (2 (2 x) + 6 y)$

Factor $2$ out of $6 y$ .

$(3 x + 4 y) (2 (2 x) + 2 (3 y))$

Factor $2$ out of $2 (2 x) + 2 (3 y)$ .

$(3 x + 4 y) (2 (2 x + 3 y))$

Remove unnecessary parentheses.

$(3 x + 4 y) \cdot 2 (2 x + 3 y)$

Factor x^2+5x(x+2y)+6(x+2y)^2

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