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

Given:

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

To do:

We have to simplify $(2x + p - c)^2 - (2x - p + c)^2$.

Solution:

We know that,

$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$

Therefore,

$(2 x+p-c)^{2}-(2 x-p+c)^{2}=[(2 x)^{2}+(p)^{2}+(-c)^{2}+2 \times 2 x \times p-2 p c-2 \times c \times 2 x]-[(2 x)^{2}+(-p)^{2}+(c)^{2}-2 \times 2 x \times p-2 p c+2 c \times 2 x]$

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

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

$=8 x p-8 c x$

$=8 x(p-c)$

Hence, $(2 x+p-c)^{2}-(2 x-p+c)^{2}=8 x(p-c)$.

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Updated on: 10-Oct-2022

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