Solve 25p^4q-100p^4q^3

$$25 p ^ { 4 } q - 100 p ^ { 4 } q ^ { 3 }$$

Factor

$$25q\left(-2q-1\right)\left(2q-1\right)p^{4}$$

Solution Steps

Factor out 25.

$$25\left(p^{4}q-4p^{4}q^{3}\right)$$

Consider p^{4}q-4p^{4}q^{3}. Factor out p^{4}q.

$$p^{4}q\left(1-4q^{2}\right)$$

Consider 1-4q^{2}. Rewrite 1-4q^{2} as 1^{2}-\left(2q\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(1-2q\right)\left(1+2q\right)$$

Reorder the terms.

$$\left(-2q+1\right)\left(2q+1\right)$$

Rewrite the complete factored expression.

$$25p^{4}q\left(-2q+1\right)\left(2q+1\right)$$

Evaluate

$$25q\left(1-4q^{2}\right)p^{4}$$