Question

Use property to evaluate: ${38}^3+(-26{)}^3+(-12{)}^3$.

• A. 34568
• B. 35567
• C. 35566
• D. 35568

Answer 1

The correct option is D 35568

Given, ${38}^3+(-26{)}^3+(-12{)}^3$
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,
$a=38$
$b=-26$
$c=-12$

$\therefore a+b+c=38-26-12=0$
Thus,
${38}^3+(-26{)}^3+(-12{)}^3$
$=3\left(38\right)(-26)(-12)$
$=35568$