Question

What's the formula for this
(x+a)^n

were x is a variable
a is a constant
and n is some power that can change example

(x+5)^2
(x+5)^3
(x+5)^4

what's the general formula?

Answer 1

(x+a)^n = x^n + nx^(n-1)a + n(n-1)/2! x^(n-2)a^2 + n(n-1)n-2)/3! x^(n-3)a^3 + ... + a^n

so (x+5)^4
= x^4 + 4x^3(5) + 4(3)/2! x^2(5^2) + 4(3)(2)/3! x(5)^3 + (4)(3)(2)(1)/4! (5)^4
= x^4 + 20x^3 + 150x^2 + 500x + 625

How about trying the others.

Answer 2

draw a tree diagram to show all the possible outcomes of tossing a coin three times?