Question

Choose the correct answers from the alternatives given.
If a = $34$, b = c = $33$, then the value of $a^3+b^3+c^3-3abc$ is

• A. $0$
• B. $111$
• C. $50$
• D. $100$

Answer 1

The correct option is D $100$

$a^3+b^3+c^3-3abc=\frac{(a+bc)}{2}\left[\right(a-b{)}^2+(b-c{)}^2+(c-d{)}^2]$
$\left(\frac{34+33+33}{2}\right)\left[\right(34-33{)}^2+(33-33{)}^2+(33-34{)}^2]$
$\frac{100}{2}\times \left[\right(1{)}^2+0+(-1{)}^2]=\frac{100}{2}(1+01)=100$