Question

Which expressions are differences of squares?

Answer 1

W² - 121
Yes we can factorize this and we will get (w + 11)(w - 11)
x² + 25
Nope, we can not factorize this
n² - 50
Again, we can not factorize this
x² - 36
Yes we can and we will get (x + 6)(x -6)

This is how I would find my answer. As you can tell, completely different compare to Apocrochon's answer but we got the same answer lol.

Thus, the correct answer are : A and D

Answer 2

If an expression is the difference of two squares, it will follow this format:
$(a)^{2}-(b)^{2}$
where a and b are integers or variables.

1) $w^{2} - 121 = (w)^{2} -( 11)^{2}$
Since the expression follows the format, it's a DoTS.

2) Since the binomial has an addition sign, it isn't a DoTS.

3) $n^{2}-50=(n)^{2}-(5\sqrt{2})^{2}$
The second term isn't an integer, so the expression isn't a DoTS.

4) $a^{2}-36=(a)^{2}-(6)^{2}$
Since the expression follows the format, it's a DoTS.

Therefore, the first and fourth expressions are differences of two squares.