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

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$x^{2} x^{2} + x^{2} x + x \cdot x^{2} + x \cdot x + x$

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.

$x^{2 + 2} + x^{2} x + x \cdot x^{2} + x \cdot x + x$

Add $2$ and $2$ .

$x^{4} + x^{2} x + x \cdot x^{2} + x \cdot x + x$

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

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

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

$x^{4} + x^{2} x^{1} + x \cdot x^{2} + x \cdot x + x$

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

$x^{4} + x^{2 + 1} + x \cdot x^{2} + x \cdot x + x$

Add $2$ and $1$ .

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

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

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

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

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

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

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

Add $1$ and $2$ .

$x^{4} + x^{3} + x^{3} + x \cdot x + x$

Multiply $x$ by $x$ .

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

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

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