The binomial theorem gives us a way to quickly expand certain binomials raised to a natural number.

Test Objectives
• Demonstrate the ability to use factorial notation
• Demonstrate the ability to evaluate a combination
• Demonstrate the ability to find the expansion of a binomial
• Demonstrate the ability to find the kth term of a binomial expansion
Binomial Theorem Practice Test:

#1:

Instructions: Evaluate each expression.

$$a)\hspace{.2em}{10 \choose 2}$$

$$b)\hspace{.2em}{9 \choose 7}$$

#2:

Instructions: Expand completely.

$$a)\hspace{.2em}(x - 2y)^4$$

$$b)\hspace{.2em}(2x + y)^6$$

#3:

Instructions: Expand completely.

$$a)\hspace{.2em}(y - 3x)^5$$

$$b)\hspace{.2em}(2x - y)^6$$

#4:

Instructions: Expand completely.

$$a)\hspace{.2em}(3y + x)^5$$

Instructions: Find each term described.

$$b)\hspace{.2em}(x - 2y)^7$$ 4th term in expansion

#5:

Instructions: Find each term described.

$$a)\hspace{.2em}(y - 2x)^6$$ 2nd term in expansion

$$b)\hspace{.2em}(x + 2y)^7$$ 6th term in expansion

Written Solutions:

#1:

Solutions:

a) 45

b) 36

#2:

Solutions:

a) x4 - 8x3y + 24x2y2 - 32xy3 + 16y4

b) 64x6 + 192x5y + 240x4y2 + 160x3y3 + 60x2y4 + 12xy5 + y6

#3:

Solutions:

a) y5 - 15y4x + 90y3x2 - 270y2x3 + 405yx4 - 243x5

b) 64x6 - 192x5y + 240x4y2 - 160x3y3 + 60x2y4 - 12xy5 + y6

#4:

Solutions:

a) 243y5 + 405y4x + 270y3x2 + 90y2x3 + 15yx4 + x5

b) -280x4y3

#5:

Solutions:

a) -12y5x

b) 672x2y5