What is (2x+5)^2-(2x-5)^2 ?

The solution to (2x+5)^2-(2x-5)^2 is 40x

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simplify (2x+5)^2-(2x-5)^2

simplify

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

40 x

Solution steps

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

Expand

(2 x + 5)^{2} : 4 x^{2} + 20 x + 25

= 4 x^{2} + 20 x + 25 - (2 x - 5)^{2}

Expand

- (2 x - 5)^{2} : - 4 x^{2} + 20 x - 25

= 4 x^{2} + 20 x + 25 - 4 x^{2} + 20 x - 25

Group like terms

= 4 x^{2} - 4 x^{2} + 20 x + 20 x + 25 - 25

Add similar elements:

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

= 20 x + 20 x + 25 - 25

Add similar elements:

20 x + 20 x = 40 x

= 40 x + 25 - 25

Subtract the numbers:

25 - 25 = 0

= 40 x

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