Question

The value of $\left(102\right)\times \left(98\right)$ is

• A. 9,992
• B. 9,994
• C. 9,996
• D. 9,998

Answer 1

The correct option is C 9,996

$\underset{–}{ConceptInvolved}$:
$(a+b)(a-b)=a^2-b^2$

$\underset{–}{Method}$:
Using the FOIL rule.
F=First terms, O= Outside terms, I = Inside terms, L= Last terms.

$\left(102\right)\times \left(98\right)=(100+2)\times (100-2)$
$=\left(100\right)\left(100\right)+\left(100\right)(-2)+\left(2\right)\left(100\right)+\left(2\right)(-2)$
$={100}^2-2\left(100\right)+2\left(100\right)-2^2$
$={100}^2+2\left(100\right)-2\left(100\right)-2^2$
$={100}^2-2^2$
$=10,000-4$
$=9,996$

This is the required expression obtained using FOIL rule.
Also, we can use the identity
$(a+b)(a-b)=a^2-b^2$.

$\left(102\right)\times \left(98\right)=(100+2)\times (100-2)$
$=(100+2)(100-2)$
$={100}^2-2^2$
$=10,000-4$
$=9,996$