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For those that struggled like me…
Going from a-z, write out the last three multiplicands.
X-X
Ah
For those of you who still struggled like me, a multiplicand in this case refers to one of the (n-x) terms.
a multiplicand in this case refers to one of the (n-x) terms
Well, that’s what was apparently meant, but in fact the correct terminology here is factors. There’s only multiplicands (and multipliers) with an explicit multiplication sign. axb - multiplicand a and multiplier b, ab - Term with factors a and b, and a is the coefficient of this Term.
For those of you who were confused even after reading the comments: (a)(b) basically means a*b. My mind just didn’t connect that to the fact that (x-x)=0. in the (a-x)(b-x) stuff is also (x-x) which = 0, and anything * 0 = 0, so no matter the value of literally everything else in the equation, it all equals out to 0 because every single () will get multiplied by (x-x), which is 0. There, hopefully that will clear it up for anyone remaining lost. And like all good jokes, they are always best when you have to explain them.
Fun fact, omitting the (x-x) zero term and expanding the entire polynomial, you’d get something with 2^25 = 33,554,432 terms. May be slightly excessive!
Couldn’t you combine a lot of like terms as you went along, though? A polynomial of the order x26 would only have 27 terms.
No, because each coefficient is its own variable; they’re not constants.
33,554,432 terms
Actually it would be that many factors. The whole thing is a single Term.
Solution?
0
There’s an (x - x) in there
Assuming both x represent the same number. There’s no reason to assume the ellipses should include x-x. Why would alphabetic order be involved at all?
duh…
