Question

Use property to evaluate :

${38}^3+{(-26)}^3+{(-12)}^3$

• A. $35968$
• B. $31268$
• C. $36668$
• D. $35568$

Answer 1

The correct option is D $35568$

${38}^3+(-26{)}^3+(-12{)}^3$
We know that
$a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-ac-bc)$
If $(a+b+c)=0$, then.
$a^3+b^3+c^3=3abc$
Here,
$a=38$
$b=-26$
$c=-12$
and $a+b+c=38+-26-12=0$
Thus,
${38}^3+(-26{)}^3+(-12{)}^3$
$=3\left(38\right)(-26)(-12)$
$=35568$