What is obtained by simplifying ( (x+2y)^2-x^2-4y^2 )?
Answer and explanation
Correct answer: \(4xy\)
Using the identity \((a+b)^2=a^2+2ab+b^2\), with \(a=x\) and \(b=2y\), we get \((x+2y)^2=x^2+4xy+4y^2\). Subtracting \(x^2\) and \(4y^2\) leaves \(4xy\). \(2xy\) is incorrect because the middle term is \(2\times x\times 2y=4xy\). Exam tip: always calculate the middle term as \(2ab\) when expanding a binomial square.
Frequently asked questions
What is the correct answer to this question?
\(4xy\)
Why is this the correct answer?
Using the identity \((a+b)^2=a^2+2ab+b^2\), with \(a=x\) and \(b=2y\), we get \((x+2y)^2=x^2+4xy+4y^2\). Subtracting \(x^2\) and \(4y^2\) leaves \(4xy\). \(2xy\) is incorrect because the middle term is \(2\times x\times 2y=4xy\). Exam tip: always calculate the middle term as \(2ab\) when expanding a binomial square.
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.
