Question

Simplify:(2a+b+c)^2+(2a-b-c)^2​

Answer 1

Answer:

hey mate

Step-by-step explanation:

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

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

4a^2+b^2+c^2+4ab+2bc+4ca+4a^2+b^2+c^2-4ab+2bc-4ca.

8a^2+2b^2+2c^2+4bc.

Answer 2

Answer:

$(2a+b+c)^{2}+(2a-b-c)^{2}=8a^{2} +4bc$

Step-by-step explanation:

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

We need to simplify the expression.

Using identity we simplify the expression:

$\begin{aligned}&(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a \\&(a-b-c)^{2}=a^{2}+b^{2}+c^{2}-2 a b+2 b c-2 c a\end{aligned}$

Using above identity the given expression is written as:

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

$=4a^{2} +b^{2}+c^{2}+4ab+2bc+4ac+4a^{2} -b^{2}-c^{2} -4ab+2bc-4ac\\=8a^{2} +4bc$

#SPJ2