Which expression can be expanded using the binomial theorem?

The third choice:  (x² - 1)³

Step-by-step explanation:

That is the only expression that is a binomial.  Binomial means "two numbers".  For this expression, x² is one number, and -1 is the other.  Choice 1 is a monomial (one number) and choices 2 and 4 are trinomials (three numbers)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4