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√(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.