Question

Find the value for ${\left(998\right)}^3$

• A. 940234942
• B. 938538392
• C. 991029942
• D. 994011992

Answer 1

The correct option is D 994011992

To find the cube of 998, we must split 998 into 2 numbers whose cubes are easy to calculate.
Hence, we write 998 as 1000 - 2.
Now,${(a–b)}^3={\left(a\right)}^3-{\left(b\right)}^3-3a^{2}b+3a{b}^2$ .
Thus, ${(1000–2)}^3$
$={\left(1000\right)}^3-{\left(2\right)}^3-3{\left(1000\right)}^2\left(2\right)+3\left(1000\right){\left(2\right)}^2$
$=994011992$