Simplify (5ab^3)(3b+11a^3-2ab)

$(5 a b^{3}) (3 b + 11 a^{3} - 2 a b)$

Step 1

Apply the distributive property.

$5 a b^{3} (3 b) + 5 a b^{3} (11 a^{3}) + 5 a b^{3} (- 2 a b)$

Step 2

Simplify.

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

Move $b$ .

$5 a (b \cdot b^{3}) \cdot 3 + 5 a b^{3} (11 a^{3}) + 5 a b^{3} (- 2 a b)$

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

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

$5 a (b^{1} b^{3}) \cdot 3 + 5 a b^{3} (11 a^{3}) + 5 a b^{3} (- 2 a b)$

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

$5 a b^{1 + 3} \cdot 3 + 5 a b^{3} (11 a^{3}) + 5 a b^{3} (- 2 a b)$

Add $1$ and $3$ .

$5 a b^{4} \cdot 3 + 5 a b^{3} (11 a^{3}) + 5 a b^{3} (- 2 a b)$

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

Move $a^{3}$ .

$5 a b^{4} \cdot 3 + 5 (a^{3} a) b^{3} \cdot 11 + 5 a b^{3} (- 2 a b)$

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

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

$5 a b^{4} \cdot 3 + 5 (a^{3} a^{1}) b^{3} \cdot 11 + 5 a b^{3} (- 2 a b)$

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

$5 a b^{4} \cdot 3 + 5 a^{3 + 1} b^{3} \cdot 11 + 5 a b^{3} (- 2 a b)$

Add $3$ and $1$ .

$5 a b^{4} \cdot 3 + 5 a^{4} b^{3} \cdot 11 + 5 a b^{3} (- 2 a b)$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$5 a b^{4} \cdot 3 + 5 a^{4} b^{3} \cdot 11 + 5 (a \cdot a) b^{3} (- 2 b)$

Multiply $a$ by $a$ .

$5 a b^{4} \cdot 3 + 5 a^{4} b^{3} \cdot 11 + 5 a^{2} b^{3} (- 2 b)$

Step 3

Simplify each term.

Multiply $3$ by $5$ .

$15 a b^{4} + 5 a^{4} b^{3} \cdot 11 + 5 a^{2} b^{3} (- 2 b)$

Multiply $11$ by $5$ .

$15 a b^{4} + 55 a^{4} b^{3} + 5 a^{2} b^{3} (- 2 b)$

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

Move $b$ .

$15 a b^{4} + 55 a^{4} b^{3} + 5 a^{2} (b \cdot b^{3}) \cdot - 2$

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

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

$15 a b^{4} + 55 a^{4} b^{3} + 5 a^{2} (b^{1} b^{3}) \cdot - 2$

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

$15 a b^{4} + 55 a^{4} b^{3} + 5 a^{2} b^{1 + 3} \cdot - 2$

Add $1$ and $3$ .

$15 a b^{4} + 55 a^{4} b^{3} + 5 a^{2} b^{4} \cdot - 2$

Multiply $- 2$ by $5$ .

$15 a b^{4} + 55 a^{4} b^{3} - 10 a^{2} b^{4}$

Simplify (5ab^3)(3b+11a^3-2ab)

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