What is the middle term in the visual expansion of a square with side (a+2b)?
Answer and explanation
Correct answer: \(4ab\)
The area of the square is \((a+2b)^2\). Using \((x+y)^2=x^2+2xy+y^2\), take \(x=a\) and \(y=2b\). The middle term is \(2\times a\times 2b=4ab\). \(2ab\) is incorrect because it does not fully include the coefficient 2 in \(2b\). Exam tip: the middle term in a binomial square is twice the product of the two terms.
Frequently asked questions
What is the correct answer to this question?
\(4ab\)
Why is this the correct answer?
The area of the square is \((a+2b)^2\). Using \((x+y)^2=x^2+2xy+y^2\), take \(x=a\) and \(y=2b\). The middle term is \(2\times a\times 2b=4ab\). \(2ab\) is incorrect because it does not fully include the coefficient 2 in \(2b\). Exam tip: the middle term in a binomial square is twice the product of the two terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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