Question

Which of the following is the expansion of (x + 3)^5?
x5 + 5x4 + 10x3 + 10x2 + 5x + 1

x5 + 3x4 + 9x3 + 27x2 + 81x + 243

x5 + 15x4 + 90x3 + 270x2 + 405x + 243

None of the above

I do not remember learning ANYTHING about this.

Answer 1

(x+3)^5 = (x+3)(x+3)(x+3)(x+3)(x+3)

Answer 2

is "I dont remember learning this an option"

Answer 3

there are formulas concerning this that make use of pascals triangle. Google pascals triangle and binomials.

Answer 4

That would be nice.. I remember Pascals Triangle, just not exactly how to use this with it.

Answer 5

The triangle of pascale gives you:
\[(x+1)^{1}=1(a)^0(x)^1+1(a)^1(x)^0\]
\[(x+a)^{2}=1(a)^0(x)^2+2(a)^1(x)^1+1(a)^2(x)^0\]
\[(x+a)^3=1(a)^0(x)^3+3(a)^1(x)^2+3(a)^2(x)^1+1(a)^3(x)^0\]
And so on. I hope you notice that the coefficent of the terms are the sum of the two directly above it (the trangle of pascale) so here it's: 1+1=2 and 1+2=3 and 2+1=3.Try expanding this to:\[ (x+a)^5\]