Question

Use property to evaluate : ${13}^3+{(-8)}^3+{(-5)}^3$

• A. $1106$
• B. $1960$
• C. $1560$
• D. $1735$

Answer 1

The correct option is C $1560$

${13}^3+(-8{)}^3+(-5{)}^3$
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,
$a=13$
$b=-8$
$c=-5$
and $a+b+c=13-8-5=0$
Thus,
${13}^3+(-8{)}^3+(-5{)}^3$
$=3\left(13\right)(-8)(-5)$
$=1560$