Chapter 14.1, Problem 1PE

a. The expanded form of ${\left(x+b\right)}^2=$ ____________. The expanded form of ${\left(a+b\right)}^3=$ ___________. These are both called expansions.

b. Given a positive integer n, the value of n! is__________. Furthermore, n! is read as “n ____________.”

c. $3!=$ ____________, $2!=$ _____________, $1!=$ ___________ and $0!=$ ____________.

d. The __________ theorem states that for any positive integer n,

${\left(a+b\right)}^n=\frac{n!}{n!\cdot 0!}{a}^n+\frac{n!}{\left(n-1\right)!\cdot 1!}{a}^{\left(n-1\right)}b+\frac{n!}{\left(n-2\right)!\cdot 2!}{a}^{\left(n-2\right)}{b}^2+\cdots +\frac{n!}{0!\cdot n!}{b}^n$.

e. The coefficients of the binomial expansion of ${\left(a+b\right)}^n$ can also be found by using ________ triangle.