Question

1.раскрыть скобки (3-у) ^6 2. Вычислить: а) Р5 б) 5!+7!/86

Answer 1

1. 18-6у

2 не знаю что имеешь ввиду

Answer 2

1. Раскрытие скобок (3-u)^6: To expand the expression (3-u)^6, you can use the binomial theorem, which states that for any positive integer n:

(x + y)^n = Σ (n choose k) * x^(n-k) * y^k

Where:

• (n choose k) is the binomial coefficient, equal to n! / (k! * (n-k)!), where n! denotes the factorial of n.
• x^(n-k) is x raised to the power of (n-k).
• y^k is y raised to the power of k.

In this case, x is 3, and y is -u. Let's proceed with the expansion:

(3-u)^6 = Σ (6 choose k) * 3^(6-k) * (-u)^k, for k = 0 to 6.

Now, let's calculate the values for k from 0 to 6 and then simplify the expression:

k = 0: (6 choose 0) * 3^6 * (-u)^0 = 1 * 729 * 1 = 729

k = 1: (6 choose 1) * 3^5 * (-u)^1 = 6 * 243 * (-u) = -1458u

k = 2: (6 choose 2) * 3^4 * (-u)^2 = 15 * 81 * u^2 = 1215u^2

k = 3: (6 choose 3) * 3^3 * (-u)^3 = 20 * 27 * (-u)^3 = -540u^3

k = 4: (6 choose 4) * 3^2 * (-u)^4 = 15 * 9 * u^4 = 135u^4

k = 5: (6 choose 5) * 3^1 * (-u)^5 = 6 * 3 * (-u)^5 = -18u^5

k = 6: (6 choose 6) * 3^0 * (-u)^6 = 1 * 1 * u^6 = u^6

Now, combine all the terms:

(3-u)^6 = 729 - 1458u + 1215u^2 - 540u^3 + 135u^4 - 18u^5 + u^6

2. Вычисление выражений: а) Р5 (P5): The notation "P5" is not standard, so I'm not sure what it refers to. If you can provide more context or clarification, I'd be happy to help with the calculation.

б) 5! + 7!/86: Let's calculate 5! (5 factorial) and 7!/86 (7 factorial divided by 86):

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040

Now, let's proceed with the expression:

5! + 7!/86 = 120 + 5040/86 ≈ 120 + 58.6047 ≈ 178.6047

So, the result is approximately 178.6047.