What is (2x+p-c)^2-(2x-p+c)^2 ?

The solution to (2x+p-c)^2-(2x-p+c)^2 is 8xp-8xc

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simplify (2x+p-c)^2-(2x-p+c)^2

simplify

(2 x + p - c)^{2} - (2 x - p + c)^{2}

8 x p - 8 x c

Solution steps

(2 x + p - c)^{2} - (2 x - p + c)^{2}

Expand

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

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

Expand

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

= 4 x^{2} - 2 p c + 4 x p - 4 x c + p^{2} + c^{2} - 4 x^{2} + 2 p c + 4 x p - 4 x c - p^{2} - c^{2}

Group like terms

= 4 x^{2} - 4 x^{2} - 2 p c + 2 p c + 4 x p + 4 x p - 4 x c - 4 x c + p^{2} - p^{2} + c^{2} - c^{2}

Add similar elements:

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

= - 2 p c + 2 p c + 4 x p + 4 x p - 4 x c - 4 x c + p^{2} - p^{2} + c^{2} - c^{2}

Add similar elements:

- 2 p c + 2 p c = 0

= 4 x p + 4 x p - 4 x c - 4 x c + p^{2} - p^{2} + c^{2} - c^{2}

Add similar elements:

4 x p + 4 x p = 8 x p

= 8 x p - 4 x c - 4 x c + p^{2} - p^{2} + c^{2} - c^{2}

Add similar elements:

- 4 x c - 4 x c = - 8 x c

= 8 x p - 8 x c + p^{2} - p^{2} + c^{2} - c^{2}

Add similar elements:

p^{2} - p^{2} = 0

= 8 x p - 8 x c + c^{2} - c^{2}

Add similar elements:

c^{2} - c^{2} = 0

= 8 x p - 8 x c

aa + 30 - 10

\frac{( 42 a \cdot b ^{4} \cdot c ^{4} )}{( 21 a ^{8} \cdot b ^{2} \cdot c ^{3} )}

\frac{t ^{- 1}}{2}

2 - 930 h^{9} - 8.002

(\frac{1}{( x + 1 )})^{3} - 3 x + sin (x)

What is (2x+p-c)^2-(2x-p+c)^2 ?
The solution to (2x+p-c)^2-(2x-p+c)^2 is 8xp-8xc