Question

Which binomial is a difference of squares?


14x2 – 81


16x2 – 81


25x2 + 81


36x3 – 81

Answer 1

So recall that a difference of squares looks something like this:
$x^{2} -4$ = (x+2)(x-2) 

Everything within the parentheses is the exact same-except for the plus and minus signs! If you multiply the first two terms (the two x's in the example above), you'll get $x^{2}$. If you multiply -2 by x and +2 by x, you'll get -2x + 2x, which equals 0 and cancel out. Then you multiply +2 by -2 to get -4. 

So in the above options, only 16$x^{2}$-81 is a difference of squares, since it simplifies down to (4x + 9)(4x - 9).