The coefficient of a term in the expansion of (a + b)^n can be found using the binomial theorem, which states that:

(a + b)^n = Σ (n choose k) * a^(n-k) * b^k

where the sum is from k = 0 to n, and "n choose k" is a binomial coefficient.

In this case, we want to find the coefficient of a^2b^3 in the expansion of (a + b)^5. This corresponds to the term where k = 3 (since b is raised to the power of 3).

So, we need to calculate "5 choose 3", which is:

5! / [3!(5-3)!] = (5*4*3*2*1) / [(3*2*1)*(2*1)] = 10

So, the coefficient of a^2b^3 in the expansion of (a + b)^5 is 10.

Question

The coefficient of a term in the expansion of (a + b)^n can be found using the binomial theorem, which states that:

(a + b)^n = Σ (n choose k) * a^(n-k) * b^k

where the sum is from k = 0 to n, and "n choose k" is a binomial coefficient.

In this case, we want to find the coefficient of a^2b^3 in the expansion of (a + b)^5. This corresponds to the term where k = 3 (since b is raised to the power of 3).

So, we need to calculate "5 choose 3", which is:

5! / [3!(5-3)!] = (5*4*3*2*1) / [(3*2*1)*(2*1)] = 10

So, the coefficient of a^2b^3 in the expansion of (a + b)^5 is 10.

Knowee AI · Accepted Answer

The coefficient of a term in the expansion of (a + b)^n can be found using the binomial theorem, which states that:

(a + b)^n = Σ (n choose k) * a^(n-k) * b^k

where the sum is from k = 0 to n, and "n choose k" is a binomial coefficient.

In this case, we want to find the coefficient of a^2b^3 in the expansion of (a + b)^5. This corresponds to the term where k = 3 (since b is raised to the power of 3).

So, we need to calculate "5 choose 3", which is:

5! / [3!(5-3)!] = (5*4*3*2*1) / [(3*2*1)*(2*1)] = 10

So, the coefficient of a^2b^3 in the expansion of (a + b)^5 is 10.

What is the coefficient of a2b3 in the expansion of (a + b)5?

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