Simplify
\[ (2x+p-c)^2-(2x-p+c)^2 \]
Solution:
Using identity:
\[ a^2-b^2=(a-b)(a+b) \]
\[ = \left[(2x+p-c)-(2x-p+c)\right] \left[(2x+p-c)+(2x-p+c)\right] \]
\[ = (2p-2c)(4x) \]
\[ = 8x(p-c) \]
\[ (2x+p-c)^2-(2x-p+c)^2 \]
Using identity:
\[ a^2-b^2=(a-b)(a+b) \]
\[ = \left[(2x+p-c)-(2x-p+c)\right] \left[(2x+p-c)+(2x-p+c)\right] \]
\[ = (2p-2c)(4x) \]
\[ = 8x(p-c) \]