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

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

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

simplify

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

8 x y

Solution steps

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

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}

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}

Group like terms

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

Add similar elements:

4 x y + 4 x y = 8 x y

= 8 x y + 4 y^{2} - 4 y^{2}

Add similar elements:

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

= 8 x y

25 s^{2} - t^{2}

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\frac{x ^{8} + x ^{4}}{2 x}