Find the Product (a^2+b)(a+b^2)

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

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

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

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

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

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

Add $1$ and $2$ .

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