25 POINTS PLUS BRAINIEST PLEASE

Using the binomial theorem , obtain the expansion of :

andrezito [222]

Answer:

see explanation

Step-by-step explanation:

Expand both factors and collect like term

Using Pascal' triangle with n = 6 to obtain the coefficients

1 6 15 20 15 6 1

Decreasing powers of 1 from $1^{6}$ to $1^{0}$

Increasing powers of 3x from $(3x)^{0}$ to $(3x)^{6}$

$1+3x)^{6}$

= 1. $1^{6}$ $(3x)^{0}$ + 6. $1^{5}$ $(3x)^{1}$ + 15. $1^{4}$ $(3x)^{2}$ + 20. $1^{3}$ $(3x)^{3}$ + 15.1² $(3x)^{4}$ + 6. $1^{1}$ $(3x)^{5}$ + 1. $1^{0}$ $(3x)^{6}$

= 1 + 18x + 135x² + 540x³ + 1215 $x^{4}$ + 1458 $x^{5}$ + 729 $x^{6}$

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$(1-3x)^{6}$

= 1. $1^{6}$ $(-3x)^{0}$ + 6. $1^{5}$ $(-3x)^{1}$ + 15. $1^{4}$ $(-3x)^{2}$ + 20. $1^{3}$ $(-3x)^{3}$ + 15.1² $(-3x)^{4}$ + 6. $1^{1}$ $(-3x)^{5}$ + 1. $1^{0}$ $(-3x)^{6}$

= 1 - 18x + 135x² - 540x³ + 1215 $x^{4}$ - 1458 $x^{5}$ + 729 $x^{6}$

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Collecting like terms from both expressions

$(1+3x)^{6}$ + $(1-3x)^{6}$

= 2 + 270x² + 2430 $x^{4}$ + 1458 $x^{6}$

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(2)

Using Pascal's triangle with n = 5

1 5 10 10 5 1

Decreasing powers of 1 from $1^{5}$ to $1^{0}$

Increasing powers of 2x from $(2x)^{0}$ to $(2x)^{5}$

$(1+2x)^{5}$

= 1. $1^{5}$ $(2x)^{0}$ + 5. $1^{4}$ $(2x)^{1}$ + 10. $1^{3}$ $(2x)^{2}$ + 10. $1^{2}$ $(2x)^{3}$ + 5. $1^{1}$ $(2x)^{4}$ + 1. $1^{0}$ $(2x)^{5}$

= 1 + 10x + 40x² + 80x³ + 80 $x^{4}$ + 32 $x^{5}$

8 0

3 years ago

Which is the directrix of a parabola with equation X^2=8y

aleksklad [387]

Alright so, After rewriting the equation in a standard parabola, you get:
4 x 2 (y-0) =(x - 0)^2

Simplify it to get:
y= 0-p
y= 0-2

When you simplify that, your answer is:
y=-2

There you go folks, just saved you from reading that long paragraph of an answer the other guy has (I don't even think the answer is in there lol, I think he just wanted to help people solve it but still most people come here for answers)

4 0

2 years ago

Marie plants 12 packages of vegetable seeds in a community garden. Each package costs $1.97. What is the total cost of the seeds

umka21 [38]

Answer:

$23.64

Step-by-step explanation:

Each package of seeds cost $1.97, and Maire bought and planted 12 packages. You would do 12 x 1.97 to get 23.64

8 0

3 years ago

Read 2 more answers

Turn and Talk How are solving 2x + 4 = 20 and 2x - 4 = 20 alike? How are they different?

hjlf

Answer:

they are both alike because you're dividing both equations by 2 . in both equations you're trying to get the variable by itself .

they are both different because both of the equations have a different x= . in equation 1 you subtract and in equation 2 you would add .

Step-by-step explanation:

For 2x+4=20 you would make +4 negative 4 to get the variable by itself .

then you'd subtract the numbers 20-4=16

then divide both sides by 2 2÷2 and 16÷2

x=8 is your answer

for 2x-4=20 you would make -4 and make it positive 4 to get the variable by itself

then you'd add the numbers 20+4

then divide both sides by 2 2÷2 and 24÷2

x=12

4 0

2 years ago

Directions: Solve these equations by using addition. You will need to use your fraction and decimal skills to solve these

Marina CMI [18]

One simple way to approach this is to subtract the number that DOESN’T have the variable with the solution by the sum.
Lets use problem 1 as the example:
1.) N+8=13
In this case, we subtract 13 by 8 and get 5, therefore N= 5.

2.) B+17=62
62-17= 45
B= 45

3.) X+5/6= 7/16
7/16-5/6= -19/48
X= -19/48

4.) y+1/7=5/8
5/8-1/7= 27/56
Y= 27/56

5.) 14+y=69
69-14=55
Y=55

6.) c+3.6=4.9
4.9-3.6=1.3
C= 1.3

Now for the word problems:
Lets use 7 as the example-
7.) a number increased by 19 is equal to 221.
Since we don’t know the number being increased by 19, that will be our variable. It will be re-written as so:

N + 19 = 221

Where N is the unknown number.

Using the same method of subtracting by the sum and the number that’s not the variable, we’ll get the solution to N
221-19= 202
N= 202

8.) N + 1 2/3 = 8
8 - 1 2/3 = 19/3= 6 1/3
N= 6 1/3

I really hope this helps

6 0

2 years ago