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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply a^{3}+a^{2}b+b^{2}a+b^{3} by a-b and combine like terms.

$$a^{4}-b^{4}-\left(a^{2}+b^{2}\right)$$

To find the opposite of a^{2}+b^{2}, find the opposite of each term.

$$a^{4}-b^{4}-a^{2}-b^{2}$$

Expand

$$a^{4}-a^{2}-b^{4}-b^{2}$$

Solution Steps

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

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

Use the distributive property to multiply a^{3}+a^{2}b+b^{2}a+b^{3} by a-b and combine like terms.

$$a^{4}-b^{4}-\left(a^{2}+b^{2}\right)$$

To find the opposite of a^{2}+b^{2}, find the opposite of each term.

$$a^{4}-b^{4}-a^{2}-b^{2}$$