Question

Find the answer
(a+b+c)^2 + (a+b-c)^2 + (a-b+c)^2​

Answer 1

Answer

(a+b+c)^2+(a-b+c)^2+(a+b-c)^2=3(a^2+b^2+c^2)+2(ac+ab-bc)

Step-by-step explanation:

Given : Expression (a+b+c)^2+(a-b+c)^2+(a+b-c)^2

To find : Simplify the expression ?

Solution :

We know that,

(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac

Similarly solve the second term,

(a-b+c)^2=a^2+(-b)^2+c^2+2a(-b)+2(-b)c+2ac

(a-b+c)^2=a^2+b^2+c^2-2ab-2bc+2ac

Similarly solve the third term,

(a+b+c)^2=a^2+b^2+(-c)^2+2ab+2b(-c)+2a(-c)

(a+b-c)^2=a^2+b^2+c^2+2ab-2bc-2ac

Substitute all in the expression,

(a+b+c)^2+(a-b+c)^2+(a+b-c)^2=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2-2ab-2bc+2ac+a^2+b^2+c^2+2ab-2bc-2ac

(a+b+c)^2+(a-b+c)^2+(a+b-c)^2=3a^2+3b^2+3c^2+2ac+2ab-2bc

(a+b+c)^2+(a-b+c)^2+(a+b-c)^2=3(a^2+b^2+c^2)+2(ac+ab-bc)

Step-by-step explanation:

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Answer 2

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