How to use the Yang Hui triangle 3x 1 to the 5th power

Coefficient. 1st power: 1

2nd power: 1 1

3rd power: 1 2 1

4 power: 1 3 3 1

5th power: 1 4 6 4 1

Count: 1 to the power a: 1 0 to the power of 1 b:

0 1 1 to the power a: 2 1 0 to the power of 1 b: 0 1 to the power of 21 a:

3 2 1 0 1 to the power b: 0 1 2 31 to the power a: 4 3 2 1 0 1 to the power b:

1 power a: 5 4 3 2 1 0 1 power b: 0 1 2 3 4 5

a+b)^5=

a 5+a 4b+a 3b 2+a 2b 3+ab 4+b 5 brings a=3x, b=1 into the algebraic equation.

Obtained original = 3x) 5+(3x) 4+(3x) 3+(3x) 2+(3x)=

243x 5+81x 4+27x 3+9x 2+3xThat's it. I may not have talked about it in my first year of junior high school.

Any questions to add?

No spaces can be punched here.

I'll use instead of .

Binomial 4 times is the number of good reeds is accompanied by positive lead 1,4,6,4,1 so: a-b) 4

a^4+4a^3.(-b)+6a^2.(-b)^2+4a(-b)^3+(-b)^4

a^4-4a^

Summary. Dear, hello, I'm glad to answer for you, x+1) The relationship between the coefficients and the Yang Hui triangle after the fourth power is as follows:

The relationship between the coefficients and the Yang Hui triangle after the fourth power of (x+1) is summarized.

Dear, hello, I'm glad to answer for you, x+1) The relationship between the coefficients and the Yang Hui triangle after the fourth power is as follows:

Analyze the terms and coefficients in the results of the cube of a+b+c. Good.

The Yang Hui triangle is a geometric arrangement of binomial coefficients in a triangle.

a+b)⁶=a⁶+6a⁵b+15a⁴b²+20a³b³+15a²b⁴+6ab⁵+b⁶.

The 5th floor of Yang Hui's three towns collapse corner is the shirt.

So (x-2y) 5=x 5+5x 4(-2y)+10x 3(-2y) 2+10x 2(-2y) 3+5x(-2y) 4+(-2y) 5

x^5-10x^4y+40x^3y^2-80x^2y^3+80xy^4-32y^5