Understanding Binomial Expansion and Coefficients

The video tutorial explains how to find the coefficient of x^5 in the expansion of two expressions: (x+2)^7 and x^3(x-3)^9. It begins by introducing the concept of binomial coefficients, n choose k, and sets up the problem. The tutorial then calculates the x^5 term in the expansion of (x+2)^7, followed by finding the x^5 term in the expansion of x^3(x-3)^9. Finally, it combines the like terms to determine the final coefficient of x^5, which is -78,648.

What is the purpose of using 'n choose k' in binomial expansions?

• To calculate the coefficient of a specific term

• To simplify the expression

• To determine the power of x

• To find the sum of coefficients

In the expansion of (x + 2)^7, what is the value of n?

• 2

• 9

• 7

• 5

What is the value of k when finding the x^5 term in (x + 2)^7?

• 9

• 7

• 5

• 2

In the expression x^3 * (x - 3)^9, what term do we need to find to contribute to x^5?

• x^2

• x^3

• x^5

• x^7

What is the value of n in the expansion of (x - 3)^9?

• 9

• 7

• 5

• 3

What is the result of 7 choose 5?

• 21

• 35

• 42

• 28

What is the result of 9 choose 2?

• 72

• 45

• 36

• 18

What is the simplified form of 21x^5 * 4?

• 84x^5

• 42x^5

• 64x^5

• 104x^5

What is the coefficient of x^5 in the expression x^3 * 36x^2 * (-2187)?

• -84,000

• -78,732

• -80,000

• -72,000

What is the final coefficient of x^5 in the given expression?

• -78,732

• -72,000

• -78,648

• -84,000