What is (2x+1)^2-(2x-1)^2 ?

The solution to (2x+1)^2-(2x-1)^2 is 8x

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simplify (2x+1)^2-(2x-1)^2

simplify

(2 x + 1)^{2} - (2 x - 1)^{2}

8 x

Solution steps

(2 x + 1)^{2} - (2 x - 1)^{2}

Expand

(2 x + 1)^{2} : 4 x^{2} + 4 x + 1

= 4 x^{2} + 4 x + 1 - (2 x - 1)^{2}

Expand

- (2 x - 1)^{2} : - 4 x^{2} + 4 x - 1

= 4 x^{2} + 4 x + 1 - 4 x^{2} + 4 x - 1

Group like terms

= 4 x^{2} - 4 x^{2} + 4 x + 4 x + 1 - 1

Add similar elements:

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

= 4 x + 4 x + 1 - 1

Add similar elements:

4 x + 4 x = 8 x

= 8 x + 1 - 1

Subtract the numbers:

1 - 1 = 0

= 8 x

(x + y i) (x - y i)

2 x \cdot (- 4)

(- 1) + 5

\frac{7}{40}

\frac{1 0 ^{3}}{1 0 ^{6}}