What is (x-2)^2-(x-4)^2 ?

The solution to (x-2)^2-(x-4)^2 is 4x-12

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simplify (x-2)^2-(x-4)^2

simplify

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

4 x - 12

Solution steps

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

Expand

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

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

Expand

- (x - 4)^{2} : - x^{2} + 8 x - 16

= x^{2} - 4 x + 4 - x^{2} + 8 x - 16

Group like terms

= x^{2} - x^{2} - 4 x + 8 x + 4 - 16

Add similar elements:

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

= - 4 x + 8 x + 4 - 16

Add similar elements:

- 4 x + 8 x = 4 x

= 4 x + 4 - 16

Subtract the numbers:

4 - 16 = - 12

= 4 x - 12

6 \times 11

6 \times 64

\frac{- 2 3}{3}

(16 x^{4})^{\frac{1}{2}}

(3 t + 1)^{2}