Factor x^2+3x(x+3y)+2(x+3y)^2

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

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

Reorder terms.

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

Reorder $2 {(x + 3 y)}^{2}$ and $3 x (x + 3 y)$ .

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

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

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

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

$x^{2} + (1 + 2) (x (x + 3 y)) + 2 {(x + 3 y)}^{2}$

Apply the distributive property.

$x^{2} + 1 (x (x + 3 y)) + 2 (x (x + 3 y)) + 2 {(x + 3 y)}^{2}$

Multiply $x (x + 3 y)$ by $1$ .

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

Remove unnecessary parentheses.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Factor the polynomial by factoring out the greatest common factor, $x + x + 3 y$ .

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

Step 2

Add $x$ and $x$ .

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $3$ by $2$ .

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

Step 5

Add $x$ and $2 x$ .

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

Step 6

Factor.

Factor $3$ out of $3 x + 6 y$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $6 y$ .

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

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

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

Remove unnecessary parentheses.

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

Factor x^2+3x(x+3y)+2(x+3y)^2

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