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

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

Simplify each term.

Expand $(a^{2} + 5 b) (a b - b^{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

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

Move $a$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $b^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $5$ by $- 1$ .

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

Reorder.

Move $b^{2}$ .

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

Move $5 b^{2}$ .

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

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

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