Simplify a^2b(3a^2+4ab^2)

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

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

Reorder.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Step 2

Simplify each term.

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

Move $a^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $a$ .

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

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

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

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

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

$3 a^{4} b + 4 a^{1 + 2} b \cdot b^{2}$

Add $1$ and $2$ .

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

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

Move $b^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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