Question #02d02

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Answer 1 · 2017-06-28T15:35:28

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

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

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...

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

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