Using the identity, what is the area of a square with side \(7+3\)?
Answer and explanation
Correct answer: \(100\)
The area of a square is the square of its side. Using \((a+b)^2=a^2+2ab+b^2\), with \(a=7\) and \(b=3\), we get \((7+3)^2=7^2+2\times7\times3+3^2=49+42+9=100\). \(49\) is only \(7^2\), so it misses both \(3\) and the middle term \(2\times7\times3\). Exam tip: for a square whose side is a sum, include all three terms: \(a^2\), \(2ab\), and \(b^2\).
Frequently asked questions
What is the correct answer to this question?
\(100\)
Why is this the correct answer?
The area of a square is the square of its side. Using \((a+b)^2=a^2+2ab+b^2\), with \(a=7\) and \(b=3\), we get \((7+3)^2=7^2+2\times7\times3+3^2=49+42+9=100\). \(49\) is only \(7^2\), so it misses both \(3\) and the middle term \(2\times7\times3\). Exam tip: for a square whose side is a sum, include all three terms: \(a^2\), \(2ab\), and \(b^2\).
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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