Question

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


20 point

Answer 1

Hi there

Your answer is :-

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

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

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

$3a^2 + 2b^2 + 2c^{2} +b^2 + 2ac + c^{2}+2ab - 2bc$

$3a^2 + 3b^2 + 2c^{2} + 2ac + c^{2}+2ab - 2bc$

$3a^2 + 3b^2 + 3c^{2} + 2ac +2ab - 2bc ( Ans )$

Thank You

Answer 2

Dear Student,

SOLUTION,

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

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

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


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

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

Answer is : $3 a^{2} + 2ab +2ac + 3 b^{2} + 3 c^{2} -2bc$


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