In an area model the sides are (3a-2) and (3a-2). What will be the total area?
Answer and explanation
Correct answer: \(9a^2-12a+4\)
The total area is \((3a-2)(3a-2)=(3a-2)^2\). Using \((x-y)^2=x^2-2xy+y^2\), with \(x=3a\) and \(y=2\), gives \(9a^2-12a+4\). Option D has a positive middle term, which would occur for \((3a+2)^2\). Exam tip: in the square of a difference, the middle term is negative.
Frequently asked questions
What is the correct answer to this question?
\(9a^2-12a+4\)
Why is this the correct answer?
The total area is \((3a-2)(3a-2)=(3a-2)^2\). Using \((x-y)^2=x^2-2xy+y^2\), with \(x=3a\) and \(y=2\), gives \(9a^2-12a+4\). Option D has a positive middle term, which would occur for \((3a+2)^2\). Exam tip: in the square of a difference, the middle term is negative.
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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