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

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

4 x y

Solution steps

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

Group like terms

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

Add similar elements:

x^{2} - x^{2} = 0

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

Add similar elements:

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

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

Add similar elements:

4 y^{2} - 4 y^{2} = 0

= 4 x y

20 x^{2}

4 a^{3} b + 10 a^{2} b^{2}

- 7 \cdot \frac{1}{4}

\frac{x ^{2}}{x ^{\frac{1}{3}}}

4 x^{2} \cdot 3 x^{2}