Can somebody please explain to me what is meant by the following question:
If $\displaystyle (8x-5)^5=Ax^5+Bx^4+Cx^3+Dx^2+Ex+F$, find $\displaystyle A+B+C+D+E+F$.
Thanks.
I'm more confused than when I posted the question. It's like I'm so confused that I don't even know what I'm confused about.
The question is from a book on basic algebra. The point the question is asked is before multiplying out parenthesis has been covered.
The answer states:
Letting $\displaystyle x = 1$ one gathers that $\displaystyle 243 = 3^5 = (8(1) - 5)^5 = A+B+C+D+E+F$.
This doesn't make any sense to me. Why 1? Why not 20: $\displaystyle 89466096875 = 155^5 = (8(20) - 5)^5 = A+B+C+D+E+F$
Should I learn from a different book? This is not the first time there's been a question like this.
Oh wow I can't believe I went about it methodically without thinking a bit more.
$\displaystyle (8x-5)^5=Ax^5+Bx^4+Cx^3+Dx^2+Ex+F$
This equality is supposed to hold for all x. If we input x = 1, we managed to make the right side into the expression in question. The left side would result in:
$\displaystyle (8(1)-5)^5 = (3)^5 = 243$
Nah, your book is fine so far. You did not need to multiply nor did you need Pascal's triangle *slaps forehead*