Simplify (4a^3b^4)(5ab^2)+(a^2b^5)(-2a^2b)

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

Simplify each term.

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

Move $a$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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

Multiply $b^{4}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

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

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

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

Add $2$ and $4$ .

$4 a^{4} b^{6} \cdot 5 + (a^{2} b^{5}) (- 2 a^{2} b)$

Multiply $5$ by $4$ .

$20 a^{4} b^{6} + (a^{2} b^{5}) (- 2 a^{2} b)$

Rewrite using the commutative property of multiplication.

$20 a^{4} b^{6} - 2 a^{2} b^{5} (a^{2} b)$

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

Move $a^{2}$ .

$20 a^{4} b^{6} - 2 (a^{2} a^{2}) b^{5} b$

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

$20 a^{4} b^{6} - 2 a^{2 + 2} b^{5} b$

Add $2$ and $2$ .

$20 a^{4} b^{6} - 2 a^{4} b^{5} b$

Multiply $b^{5}$ by $b$ by adding the exponents.

Move $b$ .

$20 a^{4} b^{6} - 2 a^{4} (b \cdot b^{5})$

Multiply $b$ by $b^{5}$ .

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

$20 a^{4} b^{6} - 2 a^{4} (b^{1} b^{5})$

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

$20 a^{4} b^{6} - 2 a^{4} b^{1 + 5}$

Add $1$ and $5$ .

$20 a^{4} b^{6} - 2 a^{4} b^{6}$

Subtract $2 a^{4} b^{6}$ from $20 a^{4} b^{6}$ .

$18 a^{4} b^{6}$