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

The solution to (x+2y)2-(x-2y)2-4xy is 8y-4xy

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

simplify

(x + 2 y) 2 - (x - 2 y) 2 - 4 x y

8 y - 4 x y

Solution steps

(x + 2 y) \cdot 2 - (x - 2 y) \cdot 2 - 4 x y

= 2 (x + 2 y) - 2 (x - 2 y) - 4 x y

Expand

2 (x + 2 y) : 2 x + 4 y

= 2 x + 4 y - 2 (x - 2 y) - 4 x y

Expand

- 2 (x - 2 y) : - 2 x + 4 y

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

Group like terms

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

Add similar elements:

2 x - 2 x = 0

= 4 y + 4 y - 4 x y

Add similar elements:

4 y + 4 y = 8 y

= 8 y - 4 x y

2 (x + y)^{2} + 5 (x + y) - 3

\frac{2}{2 + 5}

(\frac{1}{x - 2})^{2}

\frac{1}{2} \div \frac{5}{3}

\frac{1}{2} \div \frac{5}{2}