If the area model of \((3x+2)^2\) is drawn, what will be the total area of the (x)-term parts?
Answer and explanation
Correct answer: \(12x\)
In the area model, the side parts are \(3x\) and \(2\). The two rectangular regions have areas \(3x\times2=6x\) and \(2\times3x=6x\). Therefore, the total area of the x-term parts is \(6x+6x=12x\). \(9x^2\) is the area of the \(3x\times3x\) square, so it is not an x-term. Exam tip: in a square area model, remember to add both equal middle rectangles.
Frequently asked questions
What is the correct answer to this question?
\(12x\)
Why is this the correct answer?
In the area model, the side parts are \(3x\) and \(2\). The two rectangular regions have areas \(3x\times2=6x\) and \(2\times3x=6x\). Therefore, the total area of the x-term parts is \(6x+6x=12x\). \(9x^2\) is the area of the \(3x\times3x\) square, so it is not an x-term. Exam tip: in a square area model, remember to add both equal middle rectangles.
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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