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

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

Evaluate

$$a^{3}+b^{3}$$

Solution Steps

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

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

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

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

To find the opposite of ba^{2}+ab^{2}-b^{3}, find the opposite of each term.

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

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

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

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

$$a^{3}+b^{3}$$

Expand

$$a^{3}+b^{3}$$

Solution Steps

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

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

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

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

To find the opposite of ba^{2}+ab^{2}-b^{3}, find the opposite of each term.

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

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

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

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

$$a^{3}+b^{3}$$