Question

(a+b)^5Распишите и объясните по возможности

Answer 1

(a+b)^5 = a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5.

Answer 2

Expansion of (a+b)^5

To expand the expression (a+b)^5, we can use the binomial theorem. The binomial theorem states that for any positive integer n, the expansion of (a+b)^n can be written as the sum of the terms of the form C(n, k) * a^(n-k) * b^k, where C(n, k) represents the binomial coefficient.

In this case, we have (a+b)^5, so n = 5. Let's expand it step by step:

1. The first term is a^5. This term is obtained by taking a raised to the power of (5-0) and b raised to the power of 0. So, the first term is a^5.

2. The second term is C(5, 1) * a^4 * b^1. The binomial coefficient C(5, 1) is equal to 5, which represents the number of ways to choose 1 element from a set of 5 elements. So, the second term is 5 * a^4 * b.

3. The third term is C(5, 2) * a^3 * b^2. The binomial coefficient C(5, 2) is equal to 10, which represents the number of ways to choose 2 elements from a set of 5 elements. So, the third term is 10 * a^3 * b^2.

4. The fourth term is C(5, 3) * a^2 * b^3. The binomial coefficient C(5, 3) is equal to 10. So, the fourth term is 10 * a^2 * b^3.

5. The fifth term is C(5, 4) * a^1 * b^4. The binomial coefficient C(5, 4) is equal to 5. So, the fifth term is 5 * a * b^4.

6. The last term is b^5. This term is obtained by taking a raised to the power of 0 and b raised to the power of (5-0). So, the last term is b^5.

Therefore, the expansion of (a+b)^5 is:

a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5.

Please note that the terms are written in descending powers of a and ascending powers of b.