Solve {left(1/4x^2left(1/4x^2+2y^2right)right)}^2-{left(y^4-{left(1/2{x}^2+left(y-x/2right)left(y+frac{x}{2}right)right)}^2right)}^2=

$${ \left( \frac{ 1 }{ 4 } { x }^{ 2 } \left( \frac{ 1 }{ 4 } { x }^{ 2 } +2 { y }^{ 2 } \right) \right) }^{ 2 } - { \left( { y }^{ 4 } - { \left( \frac{ 1 }{ 2 } { x }^{ 2 } + \left( y- \frac{ x }{ 2 } \right) \left( y+ \frac{ x }{ 2 } \right) \right) }^{ 2 } \right) }^{ 2 } =$$

Factor

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Solution Steps

Factor out \frac{1}{256}.

$$\frac{\left(x^{2}\left(x^{2}+8y^{2}\right)\right)^{2}-\left(16y^{4}-\left(2x^{2}+\left(2y-x\right)\left(2y+x\right)\right)^{2}\right)^{2}}{256}$$

Consider \left(x^{2}\left(x^{2}+8y^{2}\right)\right)^{2}-\left(16y^{4}-\left(2x^{2}+\left(2y-x\right)\left(2y+x\right)\right)^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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Consider 2x^{4}+16x^{2}y^{2}. Factor out 2.

$$2\left(x^{4}+8x^{2}y^{2}\right)$$

Consider x^{4}+8x^{2}y^{2}. Factor out x^{2}.

$$x^{2}\left(x^{2}+8y^{2}\right)$$

Rewrite the complete factored expression.

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Evaluate

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