Solve 25x^2y^6-49x^4y^2=

$$25 x ^ { 2 } y ^ { 6 } - 49 x ^ { 4 } y ^ { 2 } =$$

Factor

$$x^{2}y^{2}\left(5y^{2}-7x\right)\left(7x+5y^{2}\right)$$

Solution Steps

Factor out x^{2}y^{2}.

$$x^{2}y^{2}\left(25y^{4}-49x^{2}\right)$$

Consider 25y^{4}-49x^{2}. Rewrite 25y^{4}-49x^{2} as \left(5y^{2}\right)^{2}-\left(7x\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5y^{2}-7x\right)\left(5y^{2}+7x\right)$$

Reorder the terms.

$$\left(-7x+5y^{2}\right)\left(7x+5y^{2}\right)$$

Rewrite the complete factored expression.

$$x^{2}y^{2}\left(-7x+5y^{2}\right)\left(7x+5y^{2}\right)$$

Evaluate

$$\left(25y^{4}-49x^{2}\right)\left(xy\right)^{2}$$