In a visual proof, ( (a+b)(c+d) ) is divided into four small rectangles. Which decomposition is correct?
Answer and explanation
Correct answer: \(ac+ad+bc+bd\)
One side of the large rectangle is \(a+b\) and the other is \(c+d\). The four smaller rectangles therefore have areas \(ac\), \(ad\), \(bc\), and \(bd\). Hence, \((a+b)(c+d)=ac+ad+bc+bd\). Option A incorrectly includes terms such as \(ab\) and \(cd\), which do not come from multiplying one part of each different side. Exam tip: in an area model, form every term by multiplying one segment from the first side by one segment from the second side.
Frequently asked questions
What is the correct answer to this question?
\(ac+ad+bc+bd\)
Why is this the correct answer?
One side of the large rectangle is \(a+b\) and the other is \(c+d\). The four smaller rectangles therefore have areas \(ac\), \(ad\), \(bc\), and \(bd\). Hence, \((a+b)(c+d)=ac+ad+bc+bd\). Option A incorrectly includes terms such as \(ab\) and \(cd\), which do not come from multiplying one part of each different side. Exam tip: in an area model, form every term by multiplying one segment from the first side by one segment from the second side.
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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