adkikani wrote:

\(\frac{(49^2 - 35^2)}{14} =\)

A. 74

B. 76

C. 78

D. 79

E. 84

\(\frac{(49^2 - 35^2)}{14}=?\)

Start writing what you know, breaking numbers into pieces: \(49^2 = (49)(49)\), for example. And there are factors of 7 everywhere.

Factor everything, with cancellation in mind if you can, to reduce errors.

\(\frac{(49)(49) - (35)(35)}{(2*7)}=\)

\(\frac{(7*7*7*7) - (7*5*7*5)}{(2*7)}=\)

Notice two 7s in numerator's two terms, hence

\(\frac{49(7*7 - 5*5)}{(2*7)}=\)

\(\frac{49(49 - 25)}{(2*7)}=\frac{49*(24)}{2*7}=\)

\(\frac{(7*7)(2*12)}{2*7}= (7*12) = 84\)

Answer E