Solve (a^{6}-b^{6}+a^{4}b^{2}-a^{2}b^{4}):(a^4+2a^2b^2+b^4)

$$( a ^ { 6 } - b ^ { 6 } + a ^ { 4 } b ^ { 2 } - a ^ { 2 } b ^ { 4 } ) : ( a ^ { 4 } + 2 a ^ { 2 } b ^ { 2 } + b ^ { 4 } )$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \left(a^{2}+b^{2}\right)^{2} in both numerator and denominator.

$$\left(a+b\right)\left(a-b\right)$$

Expand the expression.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out \left(a^{2}+b^{2}\right)^{2} in both numerator and denominator.

$$\left(a+b\right)\left(a-b\right)$$

Expand the expression.

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