Solve x^3y^4-25xd^6

$$x ^ { 3 } y ^ { 4 } - 25 x d ^ { 6 }$$

Factor

$$x\left(xy^{2}-5d^{3}\right)\left(xy^{2}+5d^{3}\right)$$

Solution Steps

Factor out x.

$$x\left(x^{2}y^{4}-25d^{6}\right)$$

Consider x^{2}y^{4}-25d^{6}. Rewrite x^{2}y^{4}-25d^{6} as \left(xy^{2}\right)^{2}-\left(5d^{3}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(xy^{2}-5d^{3}\right)\left(xy^{2}+5d^{3}\right)$$

Rewrite the complete factored expression.

$$x\left(xy^{2}-5d^{3}\right)\left(xy^{2}+5d^{3}\right)$$

Evaluate

$$x\left(x^{2}y^{4}-25d^{6}\right)$$