The binomial expansion

Which formula states the binomial theorem for a non-negative integer n?

(a+b)^n = Σ from r=0 to n of C(n,r)a^(n-r)b^r

How is the binomial coefficient C(n,r) calculated?

n factorial divided by [r factorial times (n-r) factorial]

What is the (r+1)th term in the expansion of (a+b)^n?

C(n,r)a^(n-r)b^r

How many terms appear in the standard binomial expansion of (a+b)^n before any like terms are combined?

n+1

Which recurrence relation is used to construct Pascal's triangle?

C(n,r)=C(n-1,r-1)+C(n-1,r)

Which symmetry property do binomial coefficients satisfy?

C(n,r)=C(n,n-r)

Which is the correct expansion of (x+2)^4?

x^4+8x^3+24x^2+32x+16

What is the coefficient of x^3 in the expansion of (2x-1)^5?

80

Find the coefficient of x^2 in (1+3x)^5.

90

What is the constant term in the expansion of (x^2+x^(-1))^6?

15

How do the signs behave in the expansion of (a-b)^n?

The signs alternate, beginning with a positive term

For a polynomial P(x), how can the sum of its coefficients be found?

Evaluate P(1)

For a polynomial P(x), what does P(-1) give?

The alternating sum of the coefficients

What is the middle term in the expansion of (a+b)^8?

70a^4b^4

When does the expansion of (a+b)^n have two middle terms?

When n is odd

If T_(r+1)=C(n,r)a^(n-r)b^r, which expression gives T_(r+2) divided by T_(r+1)?

[(n-r)/(r+1)](b/a)

The coefficient of x in (1+x)^n is 12. What is n?

12