1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
swat32
3 years ago
8

Using the binomial theorem , obtain the expansion of :

Mathematics
1 answer:
andrezito [222]3 years ago
8 0

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 + 1215x^{4} + 1458x^{5} + 729x^{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 + 1215x^{4} - 1458x^{5} + 729x^{6}

----------------------------------------------------------------------------------

Collecting like terms from both expressions

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

= 2 + 270x² + 2430x^{4} + 1458x^{6}

----------------------------------------------------

(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 + 80x^{4} + 32x^{5}

You might be interested in
What is the smallest unit of measurement?
kvasek [131]
The smallest unit of measure is the millimeter

Hope this helps ;)
3 0
3 years ago
Read 2 more answers
A rectangular table is 5 1/4 feet by 3 3/4 feet. What is the area of the table?
enot [183]

Answer:

19 11/16 or 315/16

Steps:

Turn the fractions into an improper fraction and then multiply straight across

5 1/4 = 21/4

3 3/4 = 15/4

(21/4)*(15/4)= 315/16= 19 11/16

Yes you got it right :)

4 0
3 years ago
Read 2 more answers
Mr. Jones waffle recipe uses 3/4 cups of milk to make 8 waffles how many cups of milk should be used to make 24 waffles?
ella [17]

Answer:

9/4

Step-by-step explanation:

If you need 3/4 cups of milk to make 8 waffles, you would need 9/4 cups to make 24 waffles because you are making 3 times the amount of waffles, so you need 3 times the amount of milk.

5 0
3 years ago
Stephen rode his bike 23.4865 miles On monday and 38.243 miles on Tuesday. How many miles did he ride in all
professor190 [17]

Answer:

61.7295 (61.7) miles

If I'm reading this correctly, this is just a simple addition equation. You'd add up 23.4865 and 38.243 to get 61.7295 miles, or 61.7 miles.

Hope I helped! ☺

6 0
2 years ago
Calculate the line integral of the vector field  F  = xy i  + (x − y) j  along C, the triangle composed of three segments. C1 is
Ksivusya [100]
Thank you for posting your question here at brianly. I hope the answer will help you. Below is the solution:

or segment from (4,0) to (-4,0), y is always zero because straight segment. 
<span>in that case x*y=x*0=0 </span>
<span>and x+y=x+0=x </span>
<span>if you choose x=4-t where t goes from 0 to 8 you should get </span>
<span>r(t)=0i+(4-t)j </span>
6 0
3 years ago
Other questions:
  • Chemistry question: What is the mass, in grams, of a sample of 6.12 × 1024 atoms of manganese (Mn)?
    15·1 answer
  • Write out the sample space for the given experiment. Use the following letters to indicate each choice: M for mushrooms, A for a
    12·1 answer
  • A piecewise function f(x) is defined as shown. f(x) = StartLayout enlarged left-brace 1st Row 1st column negative five-fourths x
    13·2 answers
  • I cant find out the unit rate can someone please draw it or help me?​
    8·1 answer
  • HELP I'M REALLY BAD AT MATH! :D
    5·2 answers
  • Karl has stamps in his desk drawer. The possible combinations of stamps are shown below.
    7·1 answer
  • Hi please help i’ll give brainliest please
    7·1 answer
  • Children. The
    13·1 answer
  • HELPPP PLEASEEEEE asappppppp
    8·1 answer
  • Was i correct pls ???? let me know and explain i'll mark brainlist :D
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!