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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply ab by a+b.

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

Use the distributive property to multiply ab by a+b.

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

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

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

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

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

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

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

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

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