Question

What should be added to 4c (-a+b+c) to obtain 3a(a+b+c) -2b(a-b+c)

Answer 1

$3a^2 + ab + 7ac -6bc + 2b^2 - 4c^2$ should be added to 4c (-a+b+c) to obtain 3a(a+b+c) -2b(a-b+c)

Solution:

Given that,

What should be added to 4c (-a+b+c) to obtain 3a(a+b+c) -2b(a-b+c)

Let "x" be the terms that should be added

Then, according to question, we get

$x + 4c(-a + b + c) = 3a(a + b + c) - 2b(a - b + c)\\\\Simplify\\\\x -4ac +4bc + 4c^2 = 3a^2 + 3ab + 3ac - 2b(a - b + c)\\\\Simplify\ further\\\\x -4ac +4bc + 4c^2 = 3a^2 + 3ab + 3ac - 2ab + 2b^2-2bc\\\\Keep\ x\ alone\ on\ left\ side\ of\ equation\\\\x = 3a^2+3ab - 2ab +3ac + 4ac -2bc -4bc + 2b^2 - 4c^2\\\\Combine\ the\ like terms\\\\x = 3a^2 + ab + 7ac -6bc + 2b^2 - 4c^2$

Thus,  $3a^2 + ab + 7ac -6bc + 2b^2 - 4c^2$ must be added to 4c (-a+b+c) to obtain 3a(a+b+c) -2b(a-b+c)

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Answer 2

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