What will be the expansion of ( (3a+b)^2 )?
Answer and explanation
Correct answer: (9a^2+6ab+b^2)
The identity \\(p+q)^2=p^2+2pq+q^2\\) helps expand a square of two terms. Here, the first term is \\(3a\\) and the second term is \\(b\\). Therefore, the expansion must contain the square of \\(3a\\), a middle term involving both terms, and the square of \\(b\\). This structure is important because the plus sign between the terms makes the middle term positive.
Substituting gives \\((3a+b)^2=(3a)^2+2(3a)(b)+b^2\\). Now, \\((3a)^2=9a^2\\) and \\(2(3a)(b)=6ab\\). Hence the result is \\(9a^2+6ab+b^2\\), which is option A. Option C misses the middle term, while option D has the wrong sign.
Frequently asked questions
What is the correct answer to this question?
(9a^2+6ab+b^2)
Why is this the correct answer?
The identity \\(p+q)^2=p^2+2pq+q^2\\) helps expand a square of two terms. Here, the first term is \\(3a\\) and the second term is \\(b\\). Therefore, the expansion must contain the square of \\(3a\\), a middle term involving both terms, and the square of \\(b\\). This structure is important because the plus sign between the terms makes the middle term positive.
Substituting gives \\((3a+b)^2=(3a)^2+2(3a)(b)+b^2\\). Now, \\((3a)^2=9a^2\\) and \\(2(3a)(b)=6ab\\). Hence the result is \\(9a^2+6ab+b^2\\), which is option A. Option C misses the middle term, while option D has the wrong sign.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
