Question

Question #02d02

Answer 1

`2a^2 + 2b^2 + 2c^2 + 4bc`

Explanation:

`[a +b+c]^2+[a-b-c]^2`

Solution

Expand the brackets..

`[a + b + c] [ a + b + c] + [a - b - c] [a - b - c]`

`[a^2 + ab + ac + ab + b^2 + bc + ac + bc + c^2] + [a^2 - ab - ac - ab + b^2 + bc - ac + bc + c^2]`

Collecting like terms...

`[a^2 + b^2 + c^2 + (ab + ab) + (ac + ac) + (bc + bc)] + [a^2 + b^2 + c^2 + (- ab - ab) + (- ac - ac) + (bc + bc) ]`

`[a^2 + b^2 + c^2 + 2ab + 2ac + 2bc] + [a^2 + b^2 + c^2 - 2ab - 2ac + 2bc]`

Collect like terms in both brackets...

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

`->` `2a^2 + 2b^2 + 2c^2 + 4bc`