Solve (x^6-y^6),(x^3+y^3)

$$( x ^ { 6 } - y ^ { 6 } ) , ( x ^ { 3 } + y ^ { 3 } )$$

Least Common Multiple

$$\left(x^{2}-y^{2}\right)\left(\left(xy\right)^{2}-\left(-x^{2}-y^{2}\right)^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{6}-y^{6}=\left(x+y\right)\left(x-y\right)\left(x^{2}-xy+y^{2}\right)\left(x^{2}+xy+y^{2}\right) x^{3}+y^{3}=\left(x+y\right)\left(x^{2}-xy+y^{2}\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(x-y\right)\left(x+y\right)\left(-x^{2}+xy-y^{2}\right)\left(x^{2}+xy+y^{2}\right)$$

Expand the expression.

$$-x^{6}+y^{6}$$

Evaluate

$$\left(x^{2}-y^{2}\right)\left(-\left(xy\right)^{2}+\left(x^{2}+y^{2}\right)^{2}\right),x^{3}+y^{3}$$