Solve 121y^8-49x^2y^4

$$121 { y }^{ 8 } -49 { x }^{ 2 } { y }^{ 4 }$$

Factor

$$\left(11y^{2}-7x\right)\left(7x+11y^{2}\right)y^{4}$$

Solution Steps

Factor out y^{4}.

$$y^{4}\left(121y^{4}-49x^{2}\right)$$

Consider 121y^{4}-49x^{2}. Rewrite 121y^{4}-49x^{2} as \left(11y^{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).

$$\left(11y^{2}-7x\right)\left(11y^{2}+7x\right)$$

Reorder the terms.

$$\left(-7x+11y^{2}\right)\left(7x+11y^{2}\right)$$

Rewrite the complete factored expression.

$$y^{4}\left(-7x+11y^{2}\right)\left(7x+11y^{2}\right)$$

Evaluate

$$y^{4}\left(121y^{4}-49x^{2}\right)$$