Solve -(a-b)(a^2+b^2)+(a+b)(a^2-2ab-b^2)

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

Evaluate

$$-4ab^{2}$$

Solution Steps

To find the opposite of a-b, find the opposite of each term.

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

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

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

Use the distributive property to multiply a+b by a^{2}-2ab-b^{2} and combine like terms.

$$-a^{3}-ab^{2}+ba^{2}+b^{3}+a^{3}-ba^{2}-3ab^{2}-b^{3}$$

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

$$-ab^{2}+ba^{2}+b^{3}-ba^{2}-3ab^{2}-b^{3}$$

Combine ba^{2} and -ba^{2} to get 0.

$$-ab^{2}+b^{3}-3ab^{2}-b^{3}$$

Combine -ab^{2} and -3ab^{2} to get -4ab^{2}.

$$-4ab^{2}+b^{3}-b^{3}$$

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

$$-4ab^{2}$$

Expand

$$-4ab^{2}$$

Solution Steps

To find the opposite of a-b, find the opposite of each term.

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

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

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

Use the distributive property to multiply a+b by a^{2}-2ab-b^{2} and combine like terms.

$$-a^{3}-ab^{2}+ba^{2}+b^{3}+a^{3}-ba^{2}-3ab^{2}-b^{3}$$

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

$$-ab^{2}+ba^{2}+b^{3}-ba^{2}-3ab^{2}-b^{3}$$

Combine ba^{2} and -ba^{2} to get 0.

$$-ab^{2}+b^{3}-3ab^{2}-b^{3}$$

Combine -ab^{2} and -3ab^{2} to get -4ab^{2}.

$$-4ab^{2}+b^{3}-b^{3}$$

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

$$-4ab^{2}$$