Solve p^2-pq+q^2,p^3+q^3,p-q

$$p ^ { 2 } - p q + q ^ { 2 } , p ^ { 3 } + q ^ { 3 } , p - q$$

Least Common Multiple

$$\left(q^{2}-p^{2}\right)\left(p^{2}-pq+q^{2}\right)$$

Solution Steps

Factor the expressions that are not already factored.

$$p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right)$$

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

$$\left(q-p\right)\left(p+q\right)\left(p^{2}-pq+q^{2}\right)$$

Expand the expression.

$$-p^{4}-pq^{3}+q^{4}+qp^{3}$$

Evaluate

$$p^{2}-pq+q^{2},p^{3}+q^{3},p-q$$