Solve 2(x-y)^2-x^4-y^4

$$2 ( x - y ) ^ { 2 } - x ^ { 4 } - y ^ { 4 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.

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

Use the distributive property to multiply 2 by x^{2}-2xy+y^{2}.

$$2x^{2}-4xy+2y^{2}-x^{4}-y^{4}$$

Expand

$$2y^{2}-y^{4}-4xy+2x^{2}-x^{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.

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

Use the distributive property to multiply 2 by x^{2}-2xy+y^{2}.

$$2x^{2}-4xy+2y^{2}-x^{4}-y^{4}$$