What is (x+y)^2+(x-y)^2 ?

The solution to (x+y)^2+(x-y)^2 is 2x^2+2y^2

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simplify (x+y)^2+(x-y)^2

simplify

(x + y)^{2} + (x - y)^{2}

2 x^{2} + 2 y^{2}

Solution steps

(x + y)^{2} + (x - y)^{2}

Expand

(x + y)^{2} : x^{2} + 2 x y + y^{2}

= x^{2} + 2 x y + y^{2} + (x - y)^{2}

Expand

(x - y)^{2} : x^{2} - 2 x y + y^{2}

= x^{2} + 2 x y + y^{2} + x^{2} - 2 x y + y^{2}

Group like terms

= x^{2} + x^{2} + 2 x y - 2 x y + y^{2} + y^{2}

Add similar elements:

x^{2} + x^{2} = 2 x^{2}

= 2 x^{2} + 2 x y - 2 x y + y^{2} + y^{2}

Add similar elements:

2 x y - 2 x y = 0

= 2 x^{2} + y^{2} + y^{2}

Add similar elements:

y^{2} + y^{2} = 2 y^{2}

= 2 x^{2} + 2 y^{2}

(8 x - 5)^{2}

(2 y^{2} + 7 y + 11) - (8 y^{2} - 5 y + 7)

(1 - x) (4 - x)

\frac{( - 1 ) ^{3}}{3}

7 \cdot 6 \cdot 5 \cdot 4