Question

If $x=3$ and $y=5$, find the value of $8x^3-12x^{2}y+6x{y}^2-8y^3$.

• A. $900$
• B. $-650$
• C. $-874$
• D. $749$

Answer 1

The correct option is C

$-874$

Observe the given expression carefully it is similiar to the expansion of the identity $(a-b{)}^3$, i.e.,

$8x^3-12x^{2}y+6x{y}^2-8y^3=(2x{)}^3-y^3-7y^3-3\times (2x{)}^2\times y+3\times 2x\times y^2=(2x-y{)}^3-7y^3$

Now, it is very easy to put the values of $x$ and $y$ in $(2x-y{)}^3-7y^3$

$\Rightarrow (2x-y{)}^3-7y^3=(2\times 3-5{)}^3-7\times 5^3$

$=1-7\times 125=-874$