Binomial questions are to be answered in detail

Find the derivatives separately.

Then assign values of 1 and -1 respectively

i.e. ((2x-3) 5).'=(a0+a1x+a2x^2+a3x^3+a4x^4+a5x^5)'

10（2x-3）^4= a1+2a2x+3a3x^2+4a4x^3+5a5x^4

Assign x=1, then a1+2a2+3a3+4a4+5a5 = 10(1+2x) 4).'=（a0+a1x+a2x^2+a3x^3+a4x^4）',8(1+2x) 3= a1+2a2x+3a3x 2+4a4x 3, and the assignment x = -1 means a1-2a2+3a3-4a4= -8

By binomial.

0 1 na+b）^n =c aº *b^n+c a¹ *b^(n-1)+.c a^n * bº

n n n Another way to do this is to make x= 0, x=1, x=-1 or something like that, but it doesn't seem to work for this problem.

1) For (2x-3) 5=a0+a1x+a2x 2+a3x 3+a4x 4+a5x 5.

10(2x-4) 4 = a1+2a2x+3a3x 2+4a4x 3+5a5x 4, so that x=1 is substituted.

a1+2a2+3a3+4a4+5a5 = 10*(-2)^4 = 160

2) For (1+2x) 4=a0+a1x+a2x 2+a3x 3+a4x 4.

8(1+2x)^3 = a1+2a2x+3a3x^2+4a4x^3

Let x=-1 be substituted.

a1-2a2+3a3-4a4=-8

The elements of the topic are incomplete, so it cannot be explained when explaining, and the topic must be complete before others can go.

So, what are the learning methods?

1. Preview. Preview is a very important learning method, through preview, you can be familiar with the content and structure of the article, in the process of preview, you can mark the place you don't understand, so that when you go to class, you can take questions, let yourself listen to the class in a targeted manner, and then improve the interest and efficiency of learning.

2. Take notes during lectures.

Listening to lectures is an important way for people to receive information. In the process of listening to the lecture, people can learn most of the content, so it is very important to grasp the lecture well. Be sure to concentrate, listen to the teacher, take notes, participate in class activities, and actively ask questions.

3. Do your homework carefully.

After the lesson, the teacher will give the students homework. The purpose of the assignment is to further consolidate what has been learned in class. So, be sure to take your homework seriously.

4. Review and summary.

After learning, you must review and summarize, through review and summary, you can make the content you learn become your own knowledge, and in the review and summary, you can find new problems and further deepen your understanding of the knowledge points.

5. Maintain self-confidence.

Self-confidence can bring great motivation to people, and only with self-confidence can we make every day more energetic and better remember what we have learned.

The front is all multiples of 8.

So the remainder of 55 55 divided by 8 is -1

So the remainder of 55 55 + 9 divided by 8 is -1 + 9 = 8, divisible by 8, so 55 55 + 9 is divisible by 8.

Question 1: The remainder is 0

1 + 3 + 3 square + 3 to the 3rd power until 3 to the 99th power = (1 + 3) + (3 2 + 3 3) + (3 4 + 3 5) ......3^96+3^97）+（3^98+3^99）

4 + 4 * (3 squared) + 4 * (3 to the fourth power) + ....4* (3 to the 98th power) is divisible by 4, so the remainder is 0

Question 2: Consider the sum of the coefficients of (a+b) to the nth power, so that a=b=1, then the sum of its coefficients is 2 to the nth power.

When the sum of the coefficients is 1024, n=10

When the power of 1/1 of the root number x is an even number, its term is an integer power, obviously, n can be used, so there are 6 terms in the formula containing the integer power of x.

I won't go into details.

1-3x) 8, the coefficients can be found by Yang Hui and Jia Xian trigonometric formulas.

Substitute the last line of numbers to get the coefficient.

1-3x)^8=

1 8-8 1 7(3x)+28 1 6x(3x) 2-56 1 5 (3x) 3+70 1 4 (3x) 4-56 1 3 (3x) 5+28x1 2 (3 ) 6-8 1 (3x) 7+(3x) 8, the coefficient is obtained.

One case is that the previous formula takes 1 and the next formula and multiplies three x terms to get x 3 terms, and the other case is that 2x 2 is taken in the previous formula, and only one x can be multiplied in the latter formula to get x 3 terms. Then merging, we get a coefficient of 12 for x 3 terms. The specific method is shown in the figure.

To clarify the definition of the number of combinations, it is easy to verify.

c stands for "combination" (not in order).

C43 is to choose 3 balls from 4 balls and take them, in the same way C41 is to choose 1 ball from 4 balls (which is equivalent to choosing 3 balls you don't want).

i.e., c43=c41