If x = 32, y = 33 and z = 35, then evaluate the expression $x^3 + y^3 +z^3 -3xyz$.
Answer & explanation
Correct answer: option 4
a3 + b3 + c3 - 3abc = \(\frac{1}{2}\)[(a + b + c) {( a- b)2 + ( b - c)2 + (c - a)2}]
If x = 32
y = 33
z = 35
Then evaluate the expression $x^3 + y^3 +z^3 -3xyz$
$x^3 + y^3 +z^3 -3xyz$ = \(\frac{1}{2}\)[(32 + 33 + 35) {( 32- 33)2 + ( 33 - 35)2 + (35 - 32)2}]
$x^3 + y^3 +z^3 -3xyz$ = \(\frac{1}{2}\)[(100) {1+ 4 + 9}]
$x^3 + y^3 +z^3 -3xyz$ = 100 × 7 = 700