If in the rectangle model of (3x+4) and (3x-4), the (3x) part is treated as the square side, what area remains?
Answer and explanation
Correct answer: \(9x^2-16\)
This rectangle model represents the identity \((a+b)(a-b)=a^2-b^2\). Here, \(a=3x\) and \(b=4\), so the area is \((3x)^2-4^2=9x^2-16\). \(9x^2+16\) may look like a sum of squares, but the product of conjugates requires subtracting 16. Exam tip: first identify the common term and the opposite constant terms.
Frequently asked questions
What is the correct answer to this question?
\(9x^2-16\)
Why is this the correct answer?
This rectangle model represents the identity \((a+b)(a-b)=a^2-b^2\). Here, \(a=3x\) and \(b=4\), so the area is \((3x)^2-4^2=9x^2-16\). \(9x^2+16\) may look like a sum of squares, but the product of conjugates requires subtracting 16. Exam tip: first identify the common term and the opposite constant 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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