Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
eBooks
General Aptitude
Arithmetic Aptitude
Data Interpretation
Show All General Aptitude
General Knowledge
Basic General Knowledge
General Science
Show All General Knowledge
Medical Science
Anatomy
Biochemical Engineering
Biochemistry
Biotechnology
Microbiology
Show All Medical Science
Technical
Database
Digital Electronics
Electronics
Networking
Show All Technical
Verbal and Reasoning
Logical Reasoning
Verbal Ability
Verbal Reasoning
Show All Verbal and Reasoning
›
What is the 3rd term in the expansion of (x + 2)^6?
What is the 3rd term in the expansion of (x + 2)^6?
Expand All
Collapse All
Practice Questions
1 question
Q1
What is the 3rd term in the expansion of (x + 2)^6?
60x^4
90x^4
120x^4
180x^4
Show Solution
Copy
The 3rd term is given by C(6, 2) * (x)^2 * (2)^4 = 15 * x^2 * 16 = 240x^2.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the 3rd term in the expansion of (x + 2)^6?
Solution:
The 3rd term is given by C(6, 2) * (x)^2 * (2)^4 = 15 * x^2 * 16 = 240x^2.
Steps: 10
Show Steps
Step 1: Identify the expression to expand, which is (x + 2)^6.
Step 2: Understand that the expansion follows the Binomial Theorem, which states that (a + b)^n = Σ [C(n, k) * a^(n-k) * b^k] for k = 0 to n.
Step 3: In our case, a = x, b = 2, and n = 6.
Step 4: We want to find the 3rd term in the expansion. The 3rd term corresponds to k = 2 (since we start counting from k = 0).
Step 5: Calculate C(6, 2), which is the number of combinations of 6 items taken 2 at a time. C(6, 2) = 6! / (2!(6-2)!) = 15.
Step 6: Calculate (x)^(6-2) = (x)^4.
Step 7: Calculate (2)^2 = 4.
Step 8: Combine these results to find the 3rd term: C(6, 2) * (x)^4 * (2)^2 = 15 * (x)^4 * 4.
Step 9: Multiply the coefficients: 15 * 4 = 60.
Step 10: Write the final result for the 3rd term: 60x^4.
Related Questions
I
If the perimeter of a rectangle is 50 cm and the length is 15 cm, what is the wi
Question: If the perimeter of a rectangle is 50 cm and the length is 15 cm, what is the width? (2020..
S
Solve for x: 3x - 7 = 2x + 5. (2021)
Question: Solve for x: 3x - 7 = 2x + 5. (2021)Options: 1211109Correct Answer: 12Exam Year: 2021Solut..
I
If the ratio of the sides of a triangle is 3:4:5, what type of triangle is it? (
Question: If the ratio of the sides of a triangle is 3:4:5, what type of triangle is it? (2019)Optio..
I
If the roots of the equation x^2 + 2x + k = 0 are -1 and -3, what is the value o
Question: If the roots of the equation x^2 + 2x + k = 0 are -1 and -3, what is the value of k? (2022..
F
Find the value of the coefficient of x^4 in the expansion of (x - 2)^6.
Question: Find the value of the coefficient of x^4 in the expansion of (x - 2)^6.Options: 15203040Co..
‹
Biology (School & UG)
Chemistry (School & UG)
Civil Engineering
Commerce & Accountancy
Computer Science & IT
Current Affairs & GK
Data Structures & Algorithms
eBooks
Electrical & Electronics Engineering
English (School)
General Aptitude
General Knowledge
General Knowledge & Current Affairs
Languages & Literature
Law & Legal Studies
Major Competitive Exams
Mathematics (School)
Mechanical Engineering
Medical Science
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Social Science (School)
Technical
Verbal and Reasoning
Vocational & Skill Development
›
Soulshift Feedback
×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy
?
0
1
2
3
4
5
6
7
8
9
10
Not likely
Very likely
✕
↑
