Simplify:$(a + b + c)^2 - (a - b + c)^2$

Given:

$(a + b + c)^2 - (a - b + c)^2$

To do:

We have to simplify $(a + b + c)^2 - (a - b + c)^2$.

Solution:

We know that,

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

Therefore,

$(a+b+c)^{2}-(a-b+c)^{2}=(a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a)-(a^{2}+b^{2}+c^{2}-2 a b-2 b c+2 c a)$

$=a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a-a^{2}-b^{2}-c^{2}+2 a b+2 b c-2 c a$

$=4 a b+4 b c$

$=4(a b+b c)$

Hence, $(a+b+c)^{2}-(a-b+c)^{2}=4(ab+bc)$. 

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

23 Views

Kickstart Your Career

Get certified by completing the course

Get Started