Question #02d02

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Question #02d02

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Answer 1 · 2017-06-28T15:35:28

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

Explanation:

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

Solution

Expand the brackets..

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

$[a^{2} + a b + a c + a b + b^{2} + b c + a c + b c + c^{2}] + [a^{2} - a b - a c - a b + b^{2} + b c - a c + b c + c^{2}]$ $[a^2 + ab + ac + ab + b^2 + bc + ac + bc + c^2] + [a^2 - ab - ac - ab + b^2 + bc - ac + bc + c^2]$

Collecting like terms...

$[a^{2} + b^{2} + c^{2} + (a b + a b) + (a c + a c) + (b c + b c)] + [a^{2} + b^{2} + c^{2} + (- a b - a b) + (- a c - a c) + (b c + b c)]$ $[a^2 + b^2 + c^2 + (ab + ab) + (ac + ac) + (bc + bc)] + [a^2 + b^2 + c^2 + (- ab - ab) + (- ac - ac) + (bc + bc) ]$

$[a^{2} + b^{2} + c^{2} + 2 a b + 2 a c + 2 b c] + [a^{2} + b^{2} + c^{2} - 2 a b - 2 a c + 2 b c]$ $[a^2 + b^2 + c^2 + 2ab + 2ac + 2bc] + [a^2 + b^2 + c^2 - 2ab - 2ac + 2bc]$

Collect like terms in both brackets...

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

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

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Question #02d02

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