Question

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

Answer 1

Step  1  : 1.1    Evaluate :  (2x+p-c)2   =  4x2+4xp-4xc+p2-2pc+c2   1.2    Evaluate :  (2x-p+c)2   =  4x2-4xp+4xc+p2-2pc+c2 

Step  2  :Pulling out like terms :

 2.1     Pull out like factors :

  8xp - 8xc  =   8x • (p - c) 

Final result : 8x • (p - c)

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Answer 2

$\textbf{\huge\underline{\underline\red{Solution} : - }}</p><p> \\ \\ \bold{ ({2x +p - c})^{2} - ({2x -p + c})^{2} } \\ \\ \bold \purple{we \: use \: formula}\\ \\ \bold \red{ {a}^{2} - {b}^{2} = {(a + b)} \: \: {(a - b)} } \\ \\ \bold {\underline \orange{let}} \\ \bold {\red{a = ({2x +p - c}) \: \: and \: \: b = ({2x -p + c})}}\\ \\ = \bold{( ({2x +p - c} )+ ({2x -p + c})) } \: \: \bold{ (({2x +p - c )-( 2x -p + c})) } \\ \\ = \bold{( {2x +p - c} + {2x - p + c}) } \: \: \bold{ ({2x +p - c -2x + p - c}) } \\ \\ = \bold {(4x) \: \: {(2p - 2c)} } \\ \\ = \fbox{\fbox{\bold \red {2((2x) \: (p - c))}}} \\ \\ \fbox{ \bold \purple{i \: hope \: it \: helps \: you.}}$