What is (u-v)^2+(u+v)^2 ?

The solution to (u-v)^2+(u+v)^2 is 2u^2+2v^2

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simplify (u-v)^2+(u+v)^2

simplify

(u - v)^{2} + (u + v)^{2}

2 u^{2} + 2 v^{2}

Solution steps

(u - v)^{2} + (u + v)^{2}

Expand

(u - v)^{2} : u^{2} - 2 uv + v^{2}

= u^{2} - 2 uv + v^{2} + (u + v)^{2}

Expand

(u + v)^{2} : u^{2} + 2 uv + v^{2}

= u^{2} - 2 uv + v^{2} + u^{2} + 2 uv + v^{2}

Group like terms

= u^{2} + u^{2} - 2 uv + 2 uv + v^{2} + v^{2}

Add similar elements:

u^{2} + u^{2} = 2 u^{2}

= 2 u^{2} - 2 uv + 2 uv + v^{2} + v^{2}

Add similar elements:

- 2 uv + 2 uv = 0

= 2 u^{2} + v^{2} + v^{2}

Add similar elements:

v^{2} + v^{2} = 2 v^{2}

= 2 u^{2} + 2 v^{2}

(- 2 f^{2} - 3 f - 5) + (- 2 f^{2} - 3 f + 8)

(x - (2 + 3 i)) (x - (2 - 3 i))

\frac{d}{d I} (x^{2} I n (x))

1^{2} + (- 1)^{2}