Question

Write a+b+c whole cube formula.

Answer 1

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Answer 2

To cube the sum of two unknown quantities, the formula we use is

$(a+b)^3=a^3+b^3+3ab(a+b)$   ---(1)  

Now we have three unknown quantities, a, b, c  

So, to get the formula for cube of the sum of three unknown quantities, we need to follow the steps

Step 1: Substitute (a+b) instead of x in (1) and z instead of y, we get

$((a+b)^3+c)^3=a^3+b^3+c^3+3(a+b)c(a+b+c)$

Step 2: Expand first term using (1)  

$((a+b)+c)^3=(a^3+b^3+3ab(a+b))+c^3+3(a+b)c(a+b+c)$    

Step 3: Bringing cube terms to LHS, we get

$(a+b+c)^3-a^3-b^3-c^3=3ab(a+b)+3(a+b)c(a+b+c)$  

$=3(a+b)[ab+c(a+b+c)]$  

$=3(a+b)[ab+c^2+ac+bc]$  

$3(a+b)[b(a+c)+c(a+c)]$  

$=3(a+b)(b+c)(a+c)$