Simplify (x^2+3x)^2+3(x^2+3x)

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

Step 1

Simplify each term.

Rewrite ${(x^{2} + 3 x)}^{2}$ as $(x^{2} + 3 x) (x^{2} + 3 x)$ .

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

Expand $(x^{2} + 3 x) (x^{2} + 3 x)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$x^{2} x^{2} + x^{2} (3 x) + 3 x \cdot x^{2} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Simplify and combine like terms.

Simplify each term.

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 2} + x^{2} (3 x) + 3 x \cdot x^{2} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Add $2$ and $2$ .

$x^{4} + x^{2} (3 x) + 3 x \cdot x^{2} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Rewrite using the commutative property of multiplication.

$x^{4} + 3 x^{2} x + 3 x \cdot x^{2} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$x^{4} + 3 (x \cdot x^{2}) + 3 x \cdot x^{2} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$x^{4} + 3 (x^{1} x^{2}) + 3 x \cdot x^{2} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} + 3 x^{1 + 2} + 3 x \cdot x^{2} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Add $1$ and $2$ .

$x^{4} + 3 x^{3} + 3 x \cdot x^{2} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$x^{4} + 3 x^{3} + 3 (x^{2} x) + 3 x (3 x) + 3 (x^{2} + 3 x)$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$x^{4} + 3 x^{3} + 3 (x^{2} x^{1}) + 3 x (3 x) + 3 (x^{2} + 3 x)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} + 3 x^{3} + 3 x^{2 + 1} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Add $2$ and $1$ .

$x^{4} + 3 x^{3} + 3 x^{3} + 3 x (3 x) + 3 (x^{2} + 3 x)$

Rewrite using the commutative property of multiplication.

$x^{4} + 3 x^{3} + 3 x^{3} + 3 \cdot 3 x \cdot x + 3 (x^{2} + 3 x)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$x^{4} + 3 x^{3} + 3 x^{3} + 3 \cdot 3 (x \cdot x) + 3 (x^{2} + 3 x)$

Multiply $x$ by $x$ .

$x^{4} + 3 x^{3} + 3 x^{3} + 3 \cdot 3 x^{2} + 3 (x^{2} + 3 x)$

Multiply $3$ by $3$ .

$x^{4} + 3 x^{3} + 3 x^{3} + 9 x^{2} + 3 (x^{2} + 3 x)$

Add $3 x^{3}$ and $3 x^{3}$ .

$x^{4} + 6 x^{3} + 9 x^{2} + 3 (x^{2} + 3 x)$

Apply the distributive property.

$x^{4} + 6 x^{3} + 9 x^{2} + 3 x^{2} + 3 (3 x)$

Multiply $3$ by $3$ .

$x^{4} + 6 x^{3} + 9 x^{2} + 3 x^{2} + 9 x$

Step 2

Add $9 x^{2}$ and $3 x^{2}$ .

$x^{4} + 6 x^{3} + 12 x^{2} + 9 x$

Simplify (x^2+3x)^2+3(x^2+3x)

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