Question

Compute the following difference

$(228\times 172)-(234\times 66)$

• A. $362$
• B. $376$
• C. $382$
• D. $372$

Answer 1

The correct option is D

$372$

The given expression is

$228\times 172-234\times 66$

$=(200+28)(200-28)-(200+34)(200-34)$

$=\left[\right(200{)}^2-\left(28{)}^2\right]-\left[\right(200{)}^2-\left(34{)}^2\right]$

$={200}^2-{28}^2-{200}^2+{34}^2$

$={34}^2-{28}^2$

$=(34+28)(34-28)$ $[a^2-b^2=(a+b\left)\right(a-b\left)\right]$

$=62\times 6$

$=372$