A rectangle has sides (p+4) and (p+7). What simplified form comes from the area model?
Answer and explanation
Correct answer: \(p^2+11p+28\)
Split the rectangle into four parts: \(p\times p=p^2\), \(p\times 7=7p\), \(4\times p=4p\), and \(4\times 7=28\). Therefore, the total area is \(p^2+7p+4p+28=p^2+11p+28\). Option C incorrectly combines \(4p\) and \(7p\). Exam tip: when multiplying two binomials, add the coefficients of the middle like terms carefully.
Frequently asked questions
What is the correct answer to this question?
\(p^2+11p+28\)
Why is this the correct answer?
Split the rectangle into four parts: \(p\times p=p^2\), \(p\times 7=7p\), \(4\times p=4p\), and \(4\times 7=28\). Therefore, the total area is \(p^2+7p+4p+28=p^2+11p+28\). Option C incorrectly combines \(4p\) and \(7p\). Exam tip: when multiplying two binomials, add the coefficients of the middle like terms 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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