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
Sergeu [11.5K]
3 years ago
13

What is the coefficient of x2y3 in the expansion of (2x + y)5?

Mathematics
1 answer:
Zigmanuir [339]3 years ago
5 0

Option C:

The coefficient of x^{2} y^{3} is 40.

Solution:

Given expression:

(2 x+y)^{5}

Using binomial theorem:

(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}

Here a=2 x, b=y

Substitute in the binomial formula, we get

(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}

                                                            $+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}

Let us solve the term one by one.

$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}

$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y

$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}

$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}

$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}

$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}

Substitute these into the above expansion.

(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}

The coefficient of x^{2} y^{3} is 40.

Option C is the correct answer.

You might be interested in
You are selling flowers for a fundraiser . You pay $ 1.50 for each flower plus a flot rate delivery fee of $ 15 . You are sellin
Feliz [49]

Answer:

15÷1 .50=10

Because you are already paying a flat rate of $15. You make 1.50 off of each flower. So you have to sell over 10 flowers to make a profit.

7 0
2 years ago
As inflation increases, it causes the money you earn today to have _____. less value in the future more purchasing power in the
Anika [276]

Answer:

This answer is A

Step-by-step explanation:

your welcome, im fast to answer

5 0
3 years ago
Read 2 more answers
Lindsay spins a spinner once and then flips a fair coin twice. The spinner is
Ivenika [448]

Answer:

3

Step-by-step explanation:

8 0
3 years ago
What is the base in the following: -55 power to 4
Alik [6]

Answer:

-55

Step-by-step explanation:

It would be -55 because the exponent is 4. So, that would leave -55 to be the right answer.

7 0
3 years ago
3) 5 fl. oz. of a 2% alcohol solution was mixed with 11 fl.
dangina [55]

Answer:

<em>The concentration of the new mixture is 46%</em>

Step-by-step explanation:

The first solution of 5 fl. oz. is concentrated at 2% alcohol. The amount of alcohol in the solution is:

5*2/100=0.1 fl. oz.

The second solution of 11 fl. oz. is 66% alcohol. The amount of alcohol in the solution is:

11*66/100=7.26 fl. oz.

The total alcohol in the mixture is

0.1 + 6.6 = 7.36 fl. oz.

The total amount of the mixture is:

5 + 11 = 16 fl.oz.

The concentration of the new mixture is:

7.36 / 16 * 100 = 46%

The concentration of the new mixture is 46%

3 0
3 years ago
Other questions:
  • 1) Find the mean of the following numbers: 5, 11, 8, 8, 7, 4, 10, 9, 7, 7, 6​
    15·1 answer
  • I need help is it A b c or d
    5·2 answers
  • Which logarithmic equation is equivalent to the exponential equation below?<br><br> 7^x=21
    11·2 answers
  • Find the surface area and volume of the following figures.
    14·2 answers
  • Eric traveled 6 miles in 15 minutes. Find the rate of speed.
    6·1 answer
  • 3.25 is what percent of 125?
    14·2 answers
  • Solve |3x + 3|= 27
    7·1 answer
  • Given (−4, 8) and (−12, 7), find the component form of the vector ⃗⃗⃗⃗⃗ .
    9·1 answer
  • 3x+4y+z=-2<br> 2y+3z=-8<br> z=-3
    9·2 answers
  • Some1 help me plus, I need this done by friday 20 points
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!