7.1 Q-28 | Mathematical Induction And Binomial Theorem | Mathematics 11

Exercise 7.1 — Question 28

Problem: Expand $(a + b)^{n}$ using the Binomial Theorem for a specific case as given in Q-28 of Exercise 7.1. (Full problem statement to be inserted here by content team.)

Binomial Theorem (Recap)

For any positive integer $n$ :

$(a + b)^{n} = \sum_{r = 0}^{n} (r n) a^{n - r} b^{r}$

where the binomial coefficient is:

$(r n) = \frac{n !}{r ! ( n - r )!}$

Key Steps for Expansion and Simplification

Identify $a$ , $b$ , and $n$ from the given expression.
Write each term using $T_{r + 1} = (r n) a^{n - r} b^{r}$ .
Simplify each term by evaluating powers and binomial coefficients.
Collect like terms if any simplification technique (e.g., substitution) is required.

Worked Solution

(Insert the specific expansion and simplification steps for Q-28 here.)

Exercise 7.1 — Question 28

Problem: Expand $(a + b)^{n}$ using the Binomial Theorem for a specific case as given in Q-28 of Exercise 7.1. (Full problem statement to be inserted here by content team.)

Binomial Theorem (Recap)

For any positive integer $n$ :

$(a + b)^{n} = \sum_{r = 0}^{n} (r n) a^{n - r} b^{r}$

where the binomial coefficient is:

$(r n) = \frac{n !}{r ! ( n - r )!}$

Key Steps for Expansion and Simplification

Identify $a$ , $b$ , and $n$ from the given expression.
Write each term using $T_{r + 1} = (r n) a^{n - r} b^{r}$ .
Simplify each term by evaluating powers and binomial coefficients.
Collect like terms if any simplification technique (e.g., substitution) is required.

Worked Solution

(Insert the specific expansion and simplification steps for Q-28 here.)