Question

Find the value of $a^3-b^3-3a^{2}b+3a{b}^2$ , when a = 5 and b = 3.

• A. 2
• B. 8
• C. 18
• D. None of these

Answer 1

The correct option is B

8

$a^3-b^3-3a^{2}b+3a{b}^2$, the given expression is the expansion of $(a-b{)}^3$

So, we have to put the values of the a = 5 and b = 3 in the given expansion

$=a^3-b^3-3a^{2}b+3a{b}^2=(a-b{)}^3=(5-3{)}^3=2^3=8$

Alternate method;
Substitute the value of a and b equal to 5 and 3 respectively in the expression $a^3-b^3-3a^{2}b+3a{b}^2$
= $5^3-3^3-3(5{)}^{2}b+3(5\left)\right(2{)}^2$
= 8