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
Rus_ich [418]
3 years ago
15

Find the 2th term of the expansion of (a-b)^4.​

Mathematics
1 answer:
vladimir1956 [14]3 years ago
3 0

The second term of the expansion is -4a^3b.

Solution:

Given expression:

(a-b)^4

To find the second term of the expansion.

(a-b)^4

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 = a and b = –b

$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}

Substitute i = 0, we get

$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4

Substitute i = 1, we get

$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b

Substitute i = 2, we get

$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}

Substitute i = 3, we get

$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}

Substitute i = 4, we get

$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}

Therefore,

$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}

=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}

Hence the second term of the expansion is -4a^3b.

You might be interested in
In the diagram, ATPR ~ AXPZ. Find the length of the altitude PY
ruslelena [56]
8.9 I am pretty sure
6 0
2 years ago
Solve this system of equations by using the elimination method -2x-2y=-6, 3x+4y=8
adoni [48]

Step-by-step explanation:

- 2x-2y=-6

3x+4y=8

multiply equation (1) by 3 and equation (2) by 2

- 6x-6y=18

6x+8y=16

Add

2y=34

y= 34÷2

y=17

substitute 17 for y in equation (2)

3x+4y=8

3x+4(17)=8

3x+68=8

3x=8-68

3x=-60

x=-60÷3

x=-20

x=-20,y=17

8 0
3 years ago
A line has a slope of -10 and includes the points (4, w) and (3,0). What is<br> the value of w?
inn [45]

Answer:

-10

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Find two consecutive integers whose product is 5 less than the square of the smaller number
S_A_V [24]
<span>
The product of -5 and -4 is 20
The square of the smaller number, -5, is 25.
The product, 20, is indeed 5 less than 25, the square of the smaller number.</span>
3 0
2 years ago
The table shows ticket prices for the local minor
Zanzabum

Answer:

2x club member ticket = 1x non-club member ticket

6 0
3 years ago
Read 2 more answers
Other questions:
  • You and your friend are standing back-to-back. Your friend runs 16 feet forward and then 12 feet right. At the same time, you ru
    7·2 answers
  • A website's views were increasing exponentially at a rate of 14% per year.
    8·2 answers
  • I need help ASAP. All the help I can get it appreciated
    9·1 answer
  • I NEEEED HELP PLEASE COMMENT IF U WILL HELP ME. ITS AN ALGEBRA QUESTION Enter your answer and show all the steps that you use to
    7·1 answer
  • During the first quarter of a game, a football team made 3 plays that each resulted in a loss
    12·1 answer
  • What is the approximate value for 83 divided 5 ?
    7·2 answers
  • Y=x^2+14x+40 in vertex form by completing the square
    5·1 answer
  • Which is a value for h h that makes the following true? -4h≥24
    9·1 answer
  • Logan invested $180 in an account paying an interest rate of 2.6% compounded continuously. Assuming no deposits or withdrawals a
    9·1 answer
  • I need help in really confused ​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!