Solve (a+b)(a^2-ab+b^2)-a(a^2+1)

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

Evaluate

$$b^{3}-a$$

Solution Steps

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

$$a^{3}+b^{3}-a\left(a^{2}+1\right)$$

Use the distributive property to multiply a by a^{2}+1.

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

To find the opposite of a^{3}+a, find the opposite of each term.

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

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

$$b^{3}-a$$

Expand

$$b^{3}-a$$

Solution Steps

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

$$a^{3}+b^{3}-a\left(a^{2}+1\right)$$

Use the distributive property to multiply a by a^{2}+1.

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

To find the opposite of a^{3}+a, find the opposite of each term.

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

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

$$b^{3}-a$$