Simplify a^2b^3(a^3+a^2b+b^2)

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Multiply $a^{2}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

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

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

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

Add $3$ and $2$ .

$a^{5} b^{3} + a^{2} b^{3} (a^{2} b) + a^{2} b^{3} b^{2}$

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

Move $a^{2}$ .

$a^{5} b^{3} + a^{2} a^{2} b^{3} b + a^{2} b^{3} b^{2}$

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

$a^{5} b^{3} + a^{2 + 2} b^{3} b + a^{2} b^{3} b^{2}$

Add $2$ and $2$ .

$a^{5} b^{3} + a^{4} b^{3} b + a^{2} b^{3} b^{2}$

Multiply $b^{3}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$a^{5} b^{3} + a^{4} b^{3} b + a^{2} (b^{2} b^{3})$

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

$a^{5} b^{3} + a^{4} b^{3} b + a^{2} b^{2 + 3}$

Add $2$ and $3$ .

$a^{5} b^{3} + a^{4} b^{3} b + a^{2} b^{5}$

Step 3

Multiply $b^{3}$ by $b$ by adding the exponents.

Move $b$ .

$a^{5} b^{3} + a^{4} (b \cdot b^{3}) + a^{2} b^{5}$

Multiply $b$ by $b^{3}$ .

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

$a^{5} b^{3} + a^{4} (b^{1} b^{3}) + a^{2} b^{5}$

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

$a^{5} b^{3} + a^{4} b^{1 + 3} + a^{2} b^{5}$

Add $1$ and $3$ .

$a^{5} b^{3} + a^{4} b^{4} + a^{2} b^{5}$