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

Related Questions

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.

180 - 109 = 71

After that you have to add what you already have (49 degrees) with what you just found (71 degrees)

49 + 71 = 120

Now that you have 120, you have to again subtract 180 by 120 to get your answer, 60 degrees. And that's it.

180 - 120 = 60

A cube has a side length of 4 feet. What is the volume of the cube?
48 ft3
64 ft3
96 ft3
12 ft3

Answers

Answer:

64 square ft^3

Step-by-step explanation:

If the side lengh is 3 then you would have 4^3 which is 64.

Answer:

64

Step-by-step explanation:

help please! ill mark brainliest!

Answers

Answer:

e=57⁰

d=104⁰

Step-by-step explanation:

in isosceles triangle the side and measures are equal

Simplify the expression 7h +(-5.9d) – 17+4d -3.4h

Please help me need it done ASAP

Answers

Answer:

−1.9d+3.6h-17

Step-by-step explanation:

You just need to combine like terms ;)

Hope it helps, let me know

f(x) = 5 – 0.2c and g(x) = 0.2(x + 5).

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:

What is the range of the function fx) = -2(6x) + 3?
(-∞,-2]
(-∞,3)
[-2,∞)
[3,∞)

Answers

the second one - (-infinity,3)

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!!

what is 3 divided by 1/5 :(

Answers

Answer:

15

Step-by-step explanation:

that's what gogle said

Answer:

15

Step-by-step explanation:

3÷1/5=3×5=15

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

What's 64/4 in the simplest form

Answers

Answer:

16

Step-by-step explanation:

64 divided by 4 is equal to 16.

64 can be divided by 4 perfectly, so 16

The distance a person can travel varies directly with the time they have been traveling if going at a constant speed. If Phoenix traveled 78 miles in 1.5 hours while going at a constant speed, how far will he travel in 2 hours at the same speed?

Answers

Answer:

answer is 175 miles, have a good day <3

How many minutes would it take a drone to travel 100 km at a speed of 40 km/min?

Answers

Answer:

Divide

Step-by-step explanation:

If you divide them then you get 2.5

Answer:

Kilometers per hour is often used for car speeds. One hour at this speed moves you 100 km

Step-by-step explanation:

i have a headache sorry if wrong

wou help video
What is the image of (-9,0) after a dilation by a scale factor of 2 centered at
the origin?

Answers

Answer:

The image is (-18,0)

Step-by-step explanation:

Here, we want to find the image of the given point after dilation by the given scale factor

Mathematically, given a point with the pre-image (x,y) going under the dilation of scale factor k, centered at the origin, the coordinates of the image will be;

(kx , ky)

Applying this in the given scenario, we have

(2(-9) , 2(0))

= (-18,0)

A grain silo is shaped like a cylinder with a height of 24 feet and a diameter of 10 feet. A farmer wishes to determine how many cubic feet of grain could fit in the silo.
What is the maximum amount of cubic feet of grain that the silo could hold?
O A 7539 cubic feet
B
2400 cubic feet
C
1884 cubic feet
O
D
600 cubic feet

Answers

Answer:

1884.95

Step-by-step explanation:

cylinder volume formula = [tex]\pi[/tex] * height * radius^2

diameter/2 = radius = 10/2 = 5

\pi * 24 * 25 = 600\pi cubic feet = 1885 when rounderd from 1884.955592

Answer:

1884

Step-by-step explanation:

find the value of x plz

Answers

It is(A) 116
As you look closely at the diagram the angle outside the angle and x are exterior angles and exterior angles are equal
It will be 61 trust me men 100%not 116

Simplify the expression so there is only one power for each base.

Answers

Answer:

Step-by-step explanation:

a (-5 + 3) = -2 ; (-7-4) = -11

solve this equation -3/4x + 6 > -3=

Answers

Answer:

[tex]x\leq 0 or x \geq \frac{1}{12}[/tex]

what is 2.006 + 6.001?

Answers

   2.006

+ 6.001

__________

   8.007

So, therefor, the answer is 8.007.

If we give the cashier a $20 bill for a shirt that costs $22.95, how much more do we owe the cashier?

Answers

Answer:

$2.95

Step-by-step explanation:

$22.95-$20

we owe the cashier $2.95

explanation:
20 - 22.95 = -2.95

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

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

find the measure of angle STP

Answers

x=7
Step-by-step explanation:
∠STP=∠SWT+∠TSW(exterrior ∠ of Δ)
15x=7x+1+7x+6
x=7

Find the volume: 7cm 16 cm 8 cm​

Answers

Answer: Greetings my dude. The volume of the triangular prism is around 1,138 Centimeters Cubed.

Hope this helps!

Answer:

volume = length * breadth * height

= 16*7*8

=896

Don Pedro tenía una parcela de 10 hectareas, vendió la quinta parte y el resto lo dividió entre sus 4 hijos, cuantas hectareas recibió cada uno?

Answers

what do i need for u supposed to help them

Pls help ASAP in a call with only my teacher

Answers

Answer:

a

Step-by-step explanation:

the answer is a. 6 faces 12 edges and 8 vertices

Answer:

I beleive it is the first option

Step-by-step explanation:

Solve

b/5 - 37 < -44

Answers

Answer:

Step-by-step explanation

B<-35

Fifteen pencils are sold for $750. what is the cost for 1 pencil ?​

Answers

One pencils cost $50
Because you to do 750/15 to get you X

Answer:

50$

Step-by-step explanation:

750/15=50

(do u mean 7.50 cuz if u did its 0.50 cents)

4x + (-3) = -11
What is my answer can You please help me

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

x=−2

Answer:

[tex]4x + ( - 3) = - 11 \\ 4x (- 3) = - 11 \\ 4x = - 11 + 3 \\ 4x = - 8 \\ x = \frac{ - 8}{4} \\ x = - 2[/tex]

Quick help please!!!

Answers

Answer:

D

Step-by-step explanation:

this isnt highschool, u are dum

When you multiply 2 decimals, how do you know where to place the comma in the product?

Answers

Answer:

you mean the decimal point?

Step-by-step explanation:

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

Answer: it would just be like putting a comma normally, just all you have to do is get your new number but then just add both the comma and decimal it shouldn’t effect on where its put! If that’s what your asking!

Step-by-step explanation:

FFFFFRrrRRreeeeeeeee PPPPOOOOOIIIINNNNTTTTTSSSSSS

Answers

Ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer:

OMG! Thank you mate..... :D

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