Binomial Expansion Coefficients

The video tutorial explains a binomial expansion problem where the coefficient of x^3 is three times that of x^2 in the expansion of (2 + 3x)^n. The teacher guides viewers through calculating the coefficients of x^3 and x^2, and then uses these to solve for the value of n. The solution involves applying the binomial theorem and simplifying the expressions. The video concludes with a call to action for viewers to share and subscribe.

What is the main task in the given binomial expansion problem?

• Expand the binomial

• Find the value of n

• Find the coefficient of x^3

• Find the coefficient of x^2

Which formula is used to find the coefficients in a binomial expansion?

• Quadratic formula

• Exponential formula

• Pythagorean theorem

• nCr formula

In the binomial expansion, what is the role of 'r' in the formula?

• It is the coefficient of the first term

• It is the total number of terms

• It is the power of the second term

• It is the power of the first term

What is the simplified expression for the coefficient of x^3?

• n(n-1)(n-2)2^n/4

• n(n-1)(n-2)2^n/8

• n(n-1)(n-2)2^n/32

• n(n-1)(n-2)2^n/16

What is the first step in finding the coefficient of x^2?

• Use the Pythagorean theorem

• Use the nCr formula

• Use the exponential formula

• Use the quadratic formula

What is the simplified expression for the coefficient of x^2?

• n(n-1)2^n/32

• n(n-1)2^n/8

• n(n-1)2^n/16

• n(n-1)2^n/4

How is the value of n determined in the problem?

• By solving a quadratic equation

• By expanding the binomial

• By using the Pythagorean theorem

• By equating the coefficients of x^3 and x^2

What is the final value of n in the binomial expansion?

• 8

• 7

• 9

• 6