Question

Using suitable identity find the value of $104\times 96$.

• A. 9962
• B. 9974
• C. 9984
• D. 9998

Answer 1

The correct option is C 9984

$\underset{–}{ConceptInvolved}$:
$(m+n)\times (m-n)$
Using the FOIL rule.
$=m\times (m-n)+n\times (m-n)$
$=m^2-mn+nm+n^2$
$=m^2+mn-nm+n^2$
We know $mn-nm=0$
$=m^2-n^2$

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

$104\times 96=(100+4)\times (100-4)$
$(100+4)\times (100-4)=100\times (100-4)+4\times (100-4)$
$={100}^2-100\cdot 4+4\cdot 100-4^2$
$={100}^2+100\cdot 4-4\cdot 100-4^2$
We know $100\cdot 4-4\cdot 100=0$
$={100}^2-4^2$
$=10,000-16$
$=9984$

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