In the expansion of (1-x ^ 2) (1 + 2x ^ 2) ^ 12, what is the coefficient of x ^ 8? The correct answer is 6160
Do you know the formula of binomial expansion? (a + b) ^ n = C (n, 0) * a ^ n + C (n, 1) * a ^ (n-1) * B + C (n, 2) a ^ (n-2) * B ^ 2 + + C(n,m)a^(n-m)b^m + …… +C (n, n) B ^ n so (1 + 2x ^ 2) ^ 12 = 1 + C (12,1) * (2x ^ 2) + C (12,2) (2x ^ 2) ^ 2 + C (12
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- 1. Find the coefficient of x ^ 4 in the expansion of (1 + x-2x ^ 2) (x + 1 / x) ^ 8
- 2. Inspired by "shower faucet", Mr. Li made up a topic: intercept the corresponding line AB from 0 to 3 on the number axis, and the real number m corresponds to the point m on AB, as shown in Figure 1; fold AB into an equilateral triangle, so that the points a and B coincide with the point P, as shown in Figure 2; establish a plane rectangular coordinate system, translate the triangle, so that it is symmetrical about the Y axis, and the coordinates of point P are (0,2), PM and X axis intersect at point n (n,0) )When m = 3, find the value of N. when you solve this problem, the value of n is () A. 4-23B. 23-4C. −233D. 233
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- 4. The teacher gave such a question and compared the product size of the following two formulas: 1] 12345x54321 2] 12344x54322 what's the thinking process
- 5. In the expansion of (1 + 2x-x ^ 2) ^ 4, find the coefficient of x ^ 7?
- 6. Factorization of 2x ^ 3-8x ^ 2 + X + 6 by undetermined coefficient method
- 7. The term with the largest coefficient in the expansion of (1 + 2x) ^ 8
- 8. If the sum of the coefficients in the expansion of (x + ax) (2x − 1x) 5 is 2, then the constant term in the expansion is () A. -40B. -20C. 20D. 40
- 9. If the coefficient sum of (x + A / x) (2x-1 / x) expansion term is 2, then the constant term is?
- 10. In the expansion of (1 + 2x) 6, the coefficient of X4 is______ .
- 11. The 96th power of 2 minus 1 can be divided by two integers between 60 and 70
- 12. If | x + Y-5 | + (xy-6) ^ 2 = 0, then x ^ 2 + y ^ 2=
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- 14. Given x + y = 5, x ^ 2 + y ^ 2 = 7, find the value of XY. Given x + y = 4, xy = 3, find the value of x ^ 2 + y ^ 2
- 15. If the square of (x + y) is 7 and the square of (X-Y) is 5, find the value of XY Given the square of X - 2x = 2, find the square of (x-1) + (x + 3) (x-3) + (x-3) (x-1)
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- 17. The known function f (x) = x & # 178; + A / X (x ≠ 0), (constant a ∈ R) (1) If f (x) is an even function, find a (2) When the constant a ≤ 16, we prove that the function f (x) increases monotonically on [2, + ∞)
- 18. If the function f (x) = x & # 178; + A / x increases in the interval [2,3], then the value range of constant a It's a process
- 19. The monotone increasing interval of function y = x-ln (5 + x ^ 2) is_____ . The answer is (- ∞, + ∞) How to calculate? If you take the derivative of Y, you should get - 2x / (5 + x ^ 2), so that the derivative is greater than 0, and you get X
- 20. The following function, which is an increasing function in the interval (0, + ∞), is () A. y=ln(x+2)B. y=−x+1C. y=(12)xD. y=x+1x