What is (x+2y)^2+(x-y)^2-4xy ?

The solution to (x+2y)^2+(x-y)^2-4xy is 2x^2-2xy+5y^2

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simplify (x+2y)^2+(x-y)^2-4xy

simplify

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

2 x^{2} - 2 x y + 5 y^{2}

Solution steps

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

Expand

(x + 2 y)^{2} : x^{2} + 4 x y + 4 y^{2}

= x^{2} + 4 x y + 4 y^{2} + (x - y)^{2} - 4 x y

Expand

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

= x^{2} + 4 x y + 4 y^{2} + x^{2} - 2 x y + y^{2} - 4 x y

Group like terms

= x^{2} + x^{2} + 4 x y - 2 x y - 4 x y + 4 y^{2} + y^{2}

Add similar elements:

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

= 2 x^{2} + 4 x y - 2 x y - 4 x y + 4 y^{2} + y^{2}

Add similar elements:

4 x y - 2 x y - 4 x y = - 2 x y

= 2 x^{2} - 2 x y + 4 y^{2} + y^{2}

Add similar elements:

4 y^{2} + y^{2} = 5 y^{2}

= 2 x^{2} - 2 x y + 5 y^{2}

\frac{( x + y )}{2}

a^{2} - b^{2} + 2 a + 1

x^{3} - 6 x^{2} - 19 x + 84

f [(\frac{- 2}{5})^{- 2}]^{3}

(\frac{a + 1}{a})^{2}

What is (x+2y)^2+(x-y)^2-4xy ?
The solution to (x+2y)^2+(x-y)^2-4xy is 2x^2-2xy+5y^2