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

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

Evaluate

$$15ba^{2}$$

Solution Steps

Use the distributive property to multiply 5ab by 3a-b.

$$15a^{2}b-5ab^{2}-b^{2}\left(4a-b\right)+b\left(4ab-b^{2}\right)+5ab^{2}$$

Use the distributive property to multiply b^{2} by 4a-b.

$$15a^{2}b-5ab^{2}-\left(4b^{2}a-b^{3}\right)+b\left(4ab-b^{2}\right)+5ab^{2}$$

To find the opposite of 4b^{2}a-b^{3}, find the opposite of each term.

$$15a^{2}b-5ab^{2}-4b^{2}a+b^{3}+b\left(4ab-b^{2}\right)+5ab^{2}$$

Combine -5ab^{2} and -4b^{2}a to get -9ab^{2}.

$$15a^{2}b-9ab^{2}+b^{3}+b\left(4ab-b^{2}\right)+5ab^{2}$$

Use the distributive property to multiply b by 4ab-b^{2}.

$$15a^{2}b-9ab^{2}+b^{3}+4ab^{2}-b^{3}+5ab^{2}$$

Combine -9ab^{2} and 4ab^{2} to get -5ab^{2}.

$$15a^{2}b-5ab^{2}+b^{3}-b^{3}+5ab^{2}$$

Combine b^{3} and -b^{3} to get 0.

$$15a^{2}b-5ab^{2}+5ab^{2}$$

Combine -5ab^{2} and 5ab^{2} to get 0.

$$15a^{2}b$$

Expand

$$15ba^{2}$$

Solution Steps

Use the distributive property to multiply 5ab by 3a-b.

$$15a^{2}b-5ab^{2}-b^{2}\left(4a-b\right)+b\left(4ab-b^{2}\right)+5ab^{2}$$

Use the distributive property to multiply b^{2} by 4a-b.

$$15a^{2}b-5ab^{2}-\left(4b^{2}a-b^{3}\right)+b\left(4ab-b^{2}\right)+5ab^{2}$$

To find the opposite of 4b^{2}a-b^{3}, find the opposite of each term.

$$15a^{2}b-5ab^{2}-4b^{2}a+b^{3}+b\left(4ab-b^{2}\right)+5ab^{2}$$

Combine -5ab^{2} and -4b^{2}a to get -9ab^{2}.

$$15a^{2}b-9ab^{2}+b^{3}+b\left(4ab-b^{2}\right)+5ab^{2}$$

Use the distributive property to multiply b by 4ab-b^{2}.

$$15a^{2}b-9ab^{2}+b^{3}+4ab^{2}-b^{3}+5ab^{2}$$

Combine -9ab^{2} and 4ab^{2} to get -5ab^{2}.

$$15a^{2}b-5ab^{2}+b^{3}-b^{3}+5ab^{2}$$

Combine b^{3} and -b^{3} to get 0.

$$15a^{2}b-5ab^{2}+5ab^{2}$$

Combine -5ab^{2} and 5ab^{2} to get 0.

$$15a^{2}b$$