Question

Compute the following differences

$(124\times 76)-(126\times 74)$

• A. 90
• B. 100
• C. 120
• D. 110

Answer 1

The correct option is B

100

The given expression

$(124\times 76)-(126\times 74)$ can be written as

$=(100+24)(100-24)-(100+26)(100-26)$

$=[{100}^2-{24}^2]-\left[\right(100{)}^2-\left(26{)}^2\right]$

$={100}^2-{24}^2-{100}^2+{26}^2$

$={26}^2-{24}^2$

$=(26+24)(26-24)$

$=50\times 2=100$