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mafiozo [28]
2 years ago
11

Expand and simplify (k-3)^7

Mathematics
2 answers:
ElenaW [278]2 years ago
4 0
(k - 3)⁷
(k - 3)(k - 3)(k - 3)(k - 3)(k - 3)(k - 3)(k - 3)
(k(k - 3) - 3(k - 3))(k(k - 3) - 3(k - 3))(k(k - 3) - 3(k - 3))(k - 3)
(k(k) - k(3) - 3(k) - 3(-3))(k(k) - k(3) - 3(k) - 3(-3))(k(k) - k(3) - 3(k) - 3(-3))(k - 3)
(k² - 3k - 3k + 9)(k² - 3k - 3k + 9)(k² - 3k - 3k + 9)(k - 3)
(k² - 6k + 9)(k² - 6k + 9)(k² - 6k + 9)(k - 3)
(k²(k² - 6k + 9) - 6k(k² - 6k + 9) + 9(k² - 6k + 9))(k²(k - 3) - 6k(k - 3) + 9(k - 3))
(k²(k²) - k²(6k) + k²(9) - 6k(k²) - 6k(-6k) - 6k(9) + 9(k²) - 9(6k) + 9(9))(k²(k) - k²(3) - 6k(k) - 6k(-3) + 9(k) - 9(3))
(k⁴ - 6k³ + 9k² - 6k³ + 36k² - 54k + 9k² - 54k + 81)(k³ - 3k² - 6k² + 18k + 9k - 27)
(k⁴ - 6k³ - 6k³ + 9k² + 36k² + 9k² - 54k - 54k - 81)(k³ - 9k² + 27k - 27)
(k⁴ - 12k³ + 54k² - 108k - 81)(k³ - 9k² + 27k - 27)
k⁴(k³ - 9k² + 27k - 27) - 12k³(k³ - 9k² + 27k² - 27) + 54k²(k³ - 9k² + 27k² - 27) - 108k(k³ - 9k² + 27k - 27) - 81(k³ - 9k² + 27k - 27)
k⁴(k³) - k⁴(9k²) + k⁴(27k) - k⁴(27) - 12k³(k³) - 12k³(-9k²) - 12k³(27k) - 12k³(-27) + 54k²(k³) - 54k²(9k²) + 54k²(27k) - 54k²(27) - 108k(k³) - 108k(9k²) - 108k(27k) - 108k(-27) - 81(k³) - 81(-9k²) - 81(27k) - 81(-27)
k⁷ - 9k⁶ + 27k⁵ - 27k⁴ - 12k⁶ + 108k⁵ - 324k⁴ + 324k³ + 54k⁵ - 486k⁴ + 1458k³ - 1458k² - 108k⁴ - 972k³ - 2916k² + 2916k - 81k³ + 729k² - 2187k + 2187
k⁷ - 9k⁶ - 12k⁶ + 27k⁵ + 108k⁵ + 54k⁵ - 27k⁴ - 324k⁴ - 486k⁴ - 108k⁴ + 324k³ + 1458k³ - 972k³ - 81k³ - 1458k² - 2196k² + 729k² + 2916k - 2187k + 2187
k⁷ - 21k⁶ + 189k⁵ - 945k⁴ + 729k³ - 2925k² + 729k + 2187
nikklg [1K]2 years ago
3 0
There are a couple of ways you can solve this. You can write it out like
(K-3)(K-3)(K-3)(K-3)(K-3)(K-3)(K-3)
And pretty much use the foil method
Or you can use the binomial theorem (google it if you dont know)
The solution should be:
(K^7) - 21(k^6) + 189(k^5) - 945(k^4) + 2835(k^3) - 5103(k^2) + 5103k - 2187
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Ariel left her home at 9 a.m., driving at 45 mph. At 11 a.m. her brother left the home and started after her at 60 mph. At what
Vlada [557]

Answer:

5:00 pm

Step-by-step explanation:

Let

x -----> the umber of hours

y ----> the total distance in miles

we know that

The distance is equal to the speed multiplied by the time

Find out the distance traveled by Ariel at 11:00 am

11:00 am-09:00 am=2 hours

45(2)=90 miles

so

<em>Ariel's linear equation is</em>

y=45x+90 ----> equation A

<em>Ariel's brother linear equation is</em>

y=60x ----> equation B

Equate equation A and equation B

60x=45x+90

Solve for x

60x-45x=90

15x=90

x=6\ hours

Adds 11:00 am + 6 hours=17:00 =5:00 pm

6 0
2 years ago
Dennis is numbering the pages of his book. Page 1 is right hand,page 2 a left hand page and faces 3,a right hand page. Which two
Aleks [24]
I drew it on paper and I got B as the pages that will face each other.

Answer: B. 22 and 23
8 0
1 year ago
6 tractors take 10days to collect the harvest. How long would it take 18 tractors to do the same amount of work?
Nutka1998 [239]
This is a question of proportionality. However, it is not direct proportionality as it is expected that as the number of tractors increases, the work is finished faster as opposed to fewer number of tractors. This is referred to as inverse proportionality.

Therefore;
6 tractors ----- 10 days
18 tractors --- x days

Then,
x = (6*10)/18 = 10/3 days = 3 days, and 8 hours.

This means that 18 tractors will take 3 days and 8 hours to collect the same harvest.
6 0
2 years ago
What is the value of k in the equation below? 5k - 2k = 12? 1 1/5, 1 5/7, 3, 4
valkas [14]
Hi there!

5k - 2k = 12
Solve for K
3k = 12
Divide both sides by 3
3k/3 = 12/3
k = 4
The correct answer is : 4


I hope that helps!
Brainliest answer :)
8 0
2 years ago
Read 2 more answers
If the point (4,-1) is a point on the graph of f then f
AlekseyPX

If the point (4,-1) is a point on the graph of y = f(x). The corresponding point on the graph of y = g(x) is: (4,-1/2), (2,-1), (-1,-1), (1,4), (4,-4), (-12,1)

  1. g(x) = \frac{1}{2} f(x) => (4,-1/2)
  2. g(x) = f(x-2) => (2,-1)
  3. g(x) = f(-x) => (-1,-1)
  4. g(x) = f(4x) => (1,4)
  5. g(x) = 4f(x) => (4,-4)
  6. g(x) = -f(x) => (-12,1)
<h3>Further explanation </h3>
  1. Dividing the function by 2 divides all the y-values by 2 as well. So to get the new point, we will take the y-value (-1) and divide it by 2 to get 2.  Therefore, the new point is  (4,-1/2)
  2. Subtracting 2 from the input of the function makes all of the x-values increase by 2 (in order to compensate for the subtraction). We will need to add 2 to the x-value (4) to get 2.  Therefore, the new point is (2,-1)
  3. Making the input of the function negative will multiply every x-value by  1.  To get the new point, we will take the x-value (4) and multiply it by -1  to get. Therefore, the new point is (-1,-1)
  4. Multiplying the input of the function by 4 makes all of the x-values be divided by 4 (in order to compensate for the multiplication). We will need to divide the x-value (4) by 4 to get 1.  Therefore, the new point is  (1,4)
  5. Multiplying the whole function by  4 increases all y-values by a factor of 4 , so the new y-value will be 4  times the original value (4) or -4.  Therefore, the new point is  (4,-4)
  6. Multiplying the whole function by -1 also multiplies every y-value by -1,  so the new y-value will be  -1 times the original value (-1). or 1. Therefore, the new point is (-12,1)

<h3>Learn more</h3>
  1. Learn more about corresponding point  brainly.com/question/10218370
  2. Learn more about point on the graph brainly.com/question/11297347
  3. Learn more about the graph brainly.com/question/11534295

<h3>Answer details</h3>

Grade:  9

Subject:  mathematics

Chapter:  corresponding point

Keywords:   corresponding point, the graph, point on the graph

3 0
2 years ago
Read 2 more answers
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