A signed rectangle model is formed by (x+3) and (x-5). What will be the total area?
Answer and explanation
Correct answer: \(x^2-2x-15\)
The four signed areas are \(x\cdot x=x^2\), \(x\cdot(-5)=-5x\), \(3\cdot x=3x\), and \(3\cdot(-5)=-15\). Adding them gives \(x^2-5x+3x-15=x^2-2x-15\). Option B incorrectly adds the two middle terms. Exam tip: multiply the constant terms for the constant term and check its sign carefully.
Frequently asked questions
What is the correct answer to this question?
\(x^2-2x-15\)
Why is this the correct answer?
The four signed areas are \(x\cdot x=x^2\), \(x\cdot(-5)=-5x\), \(3\cdot x=3x\), and \(3\cdot(-5)=-15\). Adding them gives \(x^2-5x+3x-15=x^2-2x-15\). Option B incorrectly adds the two middle terms. Exam tip: multiply the constant terms for the constant term and check its sign carefully.
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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