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

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

Evaluate

$$-b^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

Combine ab and -ab to get 0.

$$-b^{2}$$

Expand

$$-b^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

Combine ab and -ab to get 0.

$$-b^{2}$$