A rectangle has sides (2x+1) and (x+5). What is the correct expansion of the area model?
Answer and explanation
Correct answer: \(2x^2+11x+5\)
The area is split into four parts: \(2x\cdot x=2x^2\), \(2x\cdot5=10x\), \(1\cdot x=x\), and \(1\cdot5=5\). Thus, the total area is \(2x^2+10x+x+5=2x^2+11x+5\). Option A misses the \(x\) term. Exam tip: in an area model, multiply every term of one side by every term of the other side, then combine like terms.
Frequently asked questions
What is the correct answer to this question?
\(2x^2+11x+5\)
Why is this the correct answer?
The area is split into four parts: \(2x\cdot x=2x^2\), \(2x\cdot5=10x\), \(1\cdot x=x\), and \(1\cdot5=5\). Thus, the total area is \(2x^2+10x+x+5=2x^2+11x+5\). Option A misses the \(x\) term. Exam tip: in an area model, multiply every term of one side by every term of the other side, then combine like 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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