Question

Compute the following difference

$(224\times 176)-(226\times 74)$

• A. 120
• B. 100
• C. 140
• D. 80

Answer 1

The correct option is B

100

The given expression is

$224\times 176-226\times 74$

$=(200+24)(200-24)-(200+26)(200-26)$

$=\left[\right(200{)}^2-\left(24{)}^2\right]-\left[\right(200{)}^2-\left(26{)}^2\right]$

$={200}^2-{24}^2-{200}^2+{26}^2$

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

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

$=50\times 2$

$=100$