If a visual model is made for a square of side (5a-2b), what will be the expansion?
Answer and explanation
Correct answer: \(25a^2-20ab+4b^2\)
The area of a square is the square of its side. Therefore, \((5a-2b)^2=(5a)^2-2(5a)(2b)+(2b)^2=25a^2-20ab+4b^2\). The minus sign makes the middle term negative. Option B has the wrong sign in the middle term, while option C misses the factor 2. Exam tip: in \((x-y)^2=x^2-2xy+y^2\), always include 2 in the middle term.
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What is the correct answer to this question?
\(25a^2-20ab+4b^2\)
Why is this the correct answer?
The area of a square is the square of its side. Therefore, \((5a-2b)^2=(5a)^2-2(5a)(2b)+(2b)^2=25a^2-20ab+4b^2\). The minus sign makes the middle term negative. Option B has the wrong sign in the middle term, while option C misses the factor 2. Exam tip: in \((x-y)^2=x^2-2xy+y^2\), always include 2 in the middle term.
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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