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
k0ka [10]
3 years ago
11

What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10

Mathematics
1 answer:
jasenka [17]3 years ago
6 0

<u>Answer:</u>

 The coefficient of x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552

<u>Solution: </u>

The given expression is (2 x-3 y)^{10}

As per binomial theorem, we know,

(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now x^{5}\times y^5 will be the 6 term where k =5

Now, \mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}

So, the coefficient of x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right.

10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252

The coefficient of x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552

You might be interested in
Susan used 9 5/8 kilowatts of electricity to power her house for 5 1/2 hours. ON average, how many kilowatts did Susan use per h
REY [17]
The answer would be 1.75
6 0
3 years ago
I NEED HELP PLEASE EXPLAIN
kari74 [83]

Answer:

The function concerning the evolution of the value of the first car is exponential and the one concerrning the value of the second car is linear

Step-by-step explanation:

1st car's drop in value ( not considering the second hand type of drop):

1.4500$

2.4050$

3.3645$

2nd car's value is dropping 3000$ every year so the function is f(n)=45000-3000n, n- number of years

6 0
2 years ago
There plz help me is my last question and assignment
fomenos

Answer:

I believe Jamal is correct, because he is just doing it an easy way. Instead of converting the mixed number to an improper fraction he is adding the measurements step by step.

Hope it Helps!

:)

6 0
3 years ago
alison practices multiplycation for 20 minutes and divison for 10 minutes how many problems does she practice in 15 days
insens350 [35]
She dose 450. problems in 15 days
4 0
3 years ago
Read 2 more answers
Which is an equivalent ratio to 6/7?​
anastassius [24]

Answer: 12 : 14  18 : 21  24 : 28  30 : 35

Step-by-step explanation:

hope these is the right answer to your question

6 0
2 years ago
Other questions:
  • A stained glass window is shaped like a semicircle. The bottom edge of the window is 36 inches long. What is the area of the sta
    6·2 answers
  • What's the least amount 0.146, 2.0102, 0.45, 1.09, 2.001
    15·1 answer
  • Answers? Sodiejjrjejwjwkskskd
    15·1 answer
  • Ray and Cheryl each have a favor pancake recipe Ray’s recipe uses 6 3/4 cups of flour for three servings Cheryls recipe uses hal
    6·1 answer
  • Y = 2 - 2
    8·1 answer
  • Which would be the best treatment for strep throat but not diabetes?
    8·1 answer
  • A circular table has a diameter of 48 inches. A carpenter is remaking it into a square table. To the nearest tenth of an inch, w
    8·1 answer
  • Which of the following fractions is equivalent to 5/6<br><br> 10/16<br> 7/8<br> 2/3<br> 15/18
    14·2 answers
  • Is (-1,4) a solution of the inequality y&lt;2x+5?
    10·1 answer
  • Write the phrase as a numerical or algebraic expression: 7 more than 16n
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!