Ideally you should use the foil method but since time is an issue with the GRE you should probably just cheat and take a shortcut.

9x^2 - 42xy + 49y^2 is a perfect trinomial so we can use a special formula to simplify it into a binomial.

The first term will be the square root of the trinomial's first term (9x^2) which is 3x.
The second term will be the suare root of the trinomials term term (49y^2) which is 7y.
A negative sign with a positive sign gets us a negative sign.

Our binomial is hence 3x-7y.

Notice that if you multiply 3x by -7y you will get -21xy which is half of -42xy.

Answer is C.

Will it be a wrong approach to plug in different values of X and Y and land on the option D.

however, certainly the answer can be found by expanding the formula.

Plugging values is a method of elemination. Ideally one should use it when other options are not available.

Also ideally pick questions where the number of variables is low. Otherwise the number of values you need totest your hypothesis becomes too large.

For example a question with one variable can be tested with 2 or 3 points

A question with 2 variables would need 4 or 9 points (2points * 2points (4) or 3 points * 3points (9)).

In this case best avoid plugging unless you have run out of options.

Thats great advice!! thank you-- -I got your point , i'll plug in values when the variables numbers are low.

Man this is not a harder question at all, please move it to the easier one.
THANKS.

I didn't put the tag there. Usually, when I post a question I checked it out on my own.

Rarely, I put the wrong tag. For sure not hard when is easy. Moreover, more often than not is the same book that targets that question as easy,medium, hard, very hard

Thanks