Question

The value of $(98{)}^2$ is

• A. 9,601
• B. 9,602
• C. 9,603
• D. 9,604

Answer 1

The correct option is D 9,604

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

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

$(98{)}^2=(100-2{)}^2$
$(98{)}^2=(100-2\left)\right(100-2)$
Expanding terms from left to right
$=\left(100\right)(100-2)+(-2)(100-2)$
$=\left(100\right)\left(100\right)+\left(100\right)(-2)+(-2)\left(100\right)+(-2{)}^2$
$=(100{)}^2+2(100\left)\right(-2)+(-2{)}^2$
$=10,000-400+4$
$=9,604$

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

$(98{)}^2=(100-2{)}^2$
$=(100{)}^2-2(100\left)\right(2)+(2{)}^2$
$=10,000-400+4$
$=9,604$