If a model is made for a square of side (5a+2), what will be the total area?
Answer and explanation
Correct answer: \(25a^2+20a+4\)
The area of a square is the square of its side. Hence, the area of a square with side \((5a+2)\) is \((5a+2)^2\). Using \((x+y)^2=x^2+2xy+y^2\), we get \((5a+2)^2=25a^2+2(5a)(2)+4=25a^2+20a+4\). Therefore, option B is correct. Option A misses the required factor 2 in the middle term. Exam tip: when squaring a binomial, include both squared terms and the middle term \(2xy\).
Frequently asked questions
What is the correct answer to this question?
\(25a^2+20a+4\)
Why is this the correct answer?
The area of a square is the square of its side. Hence, the area of a square with side \((5a+2)\) is \((5a+2)^2\). Using \((x+y)^2=x^2+2xy+y^2\), we get \((5a+2)^2=25a^2+2(5a)(2)+4=25a^2+20a+4\). Therefore, option B is correct. Option A misses the required factor 2 in the middle term. Exam tip: when squaring a binomial, include both squared terms and the middle term \(2xy\).
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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