Mathematics High School

Using Pascal triangle, write down the binomial expansion of
[tex] {(1+y)}^{8} [/tex]
simplifying all the terms.​

Answers

Answer 1

Answer:

1 + 8y + 28y² + 56y³ + 70[tex]y^{4}[/tex] + 56[tex]y^{5}[/tex] + 28[tex]y^{6}[/tex] + 8[tex]y^{7}[/tex] + [tex]y^{8}[/tex]

Step-by-step explanation:

For the expansion of [tex](1+y)^{8}[/tex]

Using the row of Pascal's triangle for n = 8 , that is the coefficients are

1  8  28  56  70  56  28  8  1

Decreasing powers of 1 from [tex]1^{8}[/tex] to [tex]1^{0}[/tex]

Increasing powers of y from [tex]y^{0}[/tex] to [tex]y^{8}[/tex]

Then

[tex](1+y)^{8}[/tex]

= 1 . [tex]1^{8}[/tex].[tex]y^{0}[/tex] + 8. [tex]1^{7}[/tex].[tex]y^{1}[/tex] + 28. [tex]1^{6}[/tex].y² + 56. [tex]1^{5}[/tex].y³ + 70. [tex]1^{4}[/tex].[tex]y^{4}[/tex] + 56. 1³.[tex]y^{5}[/tex] + 28. 1².[tex]y^{6}[/tex] + 8. [tex]1^{1}[/tex].[tex]y^{7}[/tex] + 1. [tex]1^{0}[/tex].[tex]y^{8}[/tex]

= 1 + 8y + 28y² + 56y³ + 70[tex]y^{4}[/tex] + 56[tex]y^{5}[/tex] + 28[tex]y^{6}[/tex] + 8[tex]y^{7}[/tex] + [tex]y^{8}[/tex]

Answer 2

Answer:

y⁸ + 8y⁷ + 28y⁶ + 56y⁵ + 70y⁴ + 56y³ + 28y² + 8y + 1

Step-by-step explanation:

Given binomial

(1 + y)⁸

Expanding using Pascal triangle (attached)

Replace a and b with y and 1 in the bottom row of the triangle

(1 + y)⁸ = (y + 1)⁸ = y⁸ + 8y⁷ + 28y⁶ + 56y⁵ + 70y⁴ + 56y³ + 28y² + 8y + 1
Using Pascal Triangle, Write Down The Binomial Expansion Of [tex] {(1+y)}^{8} [/tex]simplifying All The

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Answers

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Which of the following is the correct expanded form for the series below?
4
Σ-22
»=0
O-1-2-4-8-16
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Answers

Answer:

-1-2-4-8-16

Step-by-step explanation

The solution is, 1-2 + 4-8 + 16, is the correct expanded form for the series Σ-2^n, n = 0 to 4.

What is an exponent in math?

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

given that,

the  series Σ-2^n, n = 0 to 4.

now, we have to find,

the correct expanded form for the series ,

as , we get,

the value of n = 0 to 4

so, putting the value of n = 0,1,2,3,4

we get the series as,

Σ-2^n

= -2^0 + (-2)^1 + (-2)^2 + (-2)^3 + (-2)^4

= 1 -2 + 4 - 8 +16

Hence, The solution is, 1-2 + 4-8 + 16, is the correct expanded form for the series Σ-2^n, n = 0 to 4.

To learn more on exponent number click:

brainly.com/question/19467739

#SPJ7

2. Find the measure of x.​

Answers

Answer:

x = 69 degrees

Step-by-step explanation:

180 - 146 = 34

180 - 77 - 34 = 69

x = 69 degrees

what is the answer to this question?​

Answers

Answer:

your answer will be option B

you are right

Step-by-step explanation:

have a nice day!!

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Please help me need it done ASAP

Answers

Answer:

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Step-by-step explanation:

You just need to combine like terms ;)

Hope it helps, let me know

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Answers

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Answers

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Answer:

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Step-by-step explanation:

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Answers

Answer:

i recommend math-way's they give you step by step or if you are work on Big ideas work use Slader they have all the answers  

Step-by-step explanation:

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Answers

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help please! ill mark brainliest!

Answers

Answer:

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Step-by-step explanation:

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need help asap will give brainly

Answers

Answer:

x = 60

Step-by-step explanation:

So, ever triangle, no matter what shape or size, is always going to equal 180 degrees. You start off by trying to find angle L which is 71. The way you find this is you subratch 109 from 180 which ultimately gives you 71.

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answers

Answer:

-2

Step-by-step explanation:

Let's solve your equation step-by-step

4x−3=−11

Step 1: Add 3 to both sides

4x−3+3=−11+3

4x=−8

Step 2: Divide both sides by 4

4x

4

=

−8

4

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Answer:

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Answers

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wou help video
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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

You will know when you cross the decimal point when multiplying.

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Answers

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Step-by-step explanation

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Answers

Answer:

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Answers

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Answers

Answer:

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Step-by-step explanation:

that's what gogle said

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Step-by-step explanation:

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when you want to divide by a fraction (n/d), flip the numbers and make multiply sign, but make sure always flip the second number (the number after the divide sign) and not the first and change the divide to multiply

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D

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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B
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Answers

Answer:

1884.95

Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Hope this helps!

Answer:

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