Simplify (a^2+b^2)(a+b)

$(a^{2} + b^{2}) (a + b)$

Step 1

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

Apply the distributive property.

$a^{2} (a + b) + b^{2} (a + b)$

Apply the distributive property.

$a^{2} a + a^{2} b + b^{2} (a + b)$

Apply the distributive property.

$a^{2} a + a^{2} b + b^{2} a + b^{2} b$

Step 2

Simplify terms.

Simplify each term.

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

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

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

$a^{2} a^{1} + a^{2} b + b^{2} a + b^{2} b$

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

$a^{2 + 1} + a^{2} b + b^{2} a + b^{2} b$

Add $2$ and $1$ .

$a^{3} + a^{2} b + b^{2} a + b^{2} b$

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

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

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

$a^{3} + a^{2} b + b^{2} a + b^{2} b^{1}$

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

$a^{3} + a^{2} b + b^{2} a + b^{2 + 1}$

Add $2$ and $1$ .

$a^{3} + a^{2} b + b^{2} a + b^{3}$

Reorder $b^{2}$ and $a$ .

$a^{3} + a^{2} b + a b^{2} + b^{3}$