Solve frac{a^{4}-b^{4}}{a^{2}+b^{2}-2ab}*frac{(a+b)^{2}-4ab}{a^3-b^3}diva+b/a^2+ab+b^2

$$\frac { a ^ { 4 } - b ^ { 4 } } { a ^ { 2 } + b ^ { 2 } - 2 a b } \times \frac { ( a + b ) ^ { 2 } - 4 a b } { a ^ { 3 } - b ^ { 3 } } \div \frac { a + b } { a ^ { 2 } + a b + b ^ { 2 } }$$

Evaluate

$$a^{2}+b^{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{4}-b^{4}}{a^{2}+b^{2}-2ab}.

$$\frac{\frac{\left(a+b\right)\left(a-b\right)\left(a^{2}+b^{2}\right)}{\left(a-b\right)^{2}}\times \frac{\left(a+b\right)^{2}-4ab}{a^{3}-b^{3}}}{\frac{a+b}{a^{2}+ab+b^{2}}}$$

Cancel out a-b in both numerator and denominator.

$$\frac{\frac{\left(a+b\right)\left(a^{2}+b^{2}\right)}{a-b}\times \frac{\left(a+b\right)^{2}-4ab}{a^{3}-b^{3}}}{\frac{a+b}{a^{2}+ab+b^{2}}}$$

Factor the expressions that are not already factored in \frac{\left(a+b\right)^{2}-4ab}{a^{3}-b^{3}}.

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

Cancel out a-b in both numerator and denominator.

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

Multiply \frac{\left(a+b\right)\left(a^{2}+b^{2}\right)}{a-b} times \frac{a-b}{a^{2}+ab+b^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a-b in both numerator and denominator.

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

Divide \frac{\left(a+b\right)\left(a^{2}+b^{2}\right)}{a^{2}+ab+b^{2}} by \frac{a+b}{a^{2}+ab+b^{2}} by multiplying \frac{\left(a+b\right)\left(a^{2}+b^{2}\right)}{a^{2}+ab+b^{2}} by the reciprocal of \frac{a+b}{a^{2}+ab+b^{2}}.

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

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

$$a^{2}+b^{2}$$

Expand

$$a^{2}+b^{2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{4}-b^{4}}{a^{2}+b^{2}-2ab}.

$$\frac{\frac{\left(a+b\right)\left(a-b\right)\left(a^{2}+b^{2}\right)}{\left(a-b\right)^{2}}\times \frac{\left(a+b\right)^{2}-4ab}{a^{3}-b^{3}}}{\frac{a+b}{a^{2}+ab+b^{2}}}$$

Cancel out a-b in both numerator and denominator.

$$\frac{\frac{\left(a+b\right)\left(a^{2}+b^{2}\right)}{a-b}\times \frac{\left(a+b\right)^{2}-4ab}{a^{3}-b^{3}}}{\frac{a+b}{a^{2}+ab+b^{2}}}$$

Factor the expressions that are not already factored in \frac{\left(a+b\right)^{2}-4ab}{a^{3}-b^{3}}.

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

Cancel out a-b in both numerator and denominator.

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

Multiply \frac{\left(a+b\right)\left(a^{2}+b^{2}\right)}{a-b} times \frac{a-b}{a^{2}+ab+b^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out a-b in both numerator and denominator.

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

Divide \frac{\left(a+b\right)\left(a^{2}+b^{2}\right)}{a^{2}+ab+b^{2}} by \frac{a+b}{a^{2}+ab+b^{2}} by multiplying \frac{\left(a+b\right)\left(a^{2}+b^{2}\right)}{a^{2}+ab+b^{2}} by the reciprocal of \frac{a+b}{a^{2}+ab+b^{2}}.

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

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

$$a^{2}+b^{2}$$