Question

Раскрыть скобки в выражении: (a+b)^8

Answer 1

(a+b)*8=8a+8b

Вот это решение

Answer 2

To expand the expression (a + b)^8, we can use the binomial theorem. The binomial theorem states that for any positive integer n:

(a + b)^n = Σ(i = 0 to n) [nCi * (a^(n-i)) * (b^i)]

where nCi is the binomial coefficient, given by nCi = n! / (i! * (n-i)!), and "!" denotes the factorial of a number.

In the case of (a + b)^8, n = 8. So, we have:

(a + b)^8 = Σ(i = 0 to 8) [8Ci * (a^(8-i)) * (b^i)]

Now, let's calculate the values of (8Ci) for i = 0 to 8:

8C0 = 8! / (0! * (8-0)!) = 1 8C1 = 8! / (1! * (8-1)!) = 8 8C2 = 8! / (2! * (8-2)!) = 28 8C3 = 8! / (3! * (8-3)!) = 56 8C4 = 8! / (4! * (8-4)!) = 70 8C5 = 8! / (5! * (8-5)!) = 56 8C6 = 8! / (6! * (8-6)!) = 28 8C7 = 8! / (7! * (8-7)!) = 8 8C8 = 8! / (8! * (8-8)!) = 1

Now, we can substitute these values into the formula:

(a + b)^8 = 1a^8b^0 + 8a^7b^1 + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a^3b^5 + 28a^2b^6 + 8a^1b^7 + 1a^0b^8

Simplifying further:

(a + b)^8 = a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a^3b^5 + 28a^2b^6 + 8ab^7 + b^8

So, the expanded form of (a + b)^8 is: a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a^3b^5 + 28a^2b^6 + 8ab^7 + b^8