If a visual model is made for a square of side (2a-b), what will be the expansion?
Answer and explanation
Correct answer: (4a^2-4ab+b^2)
The area of a square is the square of its side. For side \\(2a-b\\), the area is \\((2a-b)^2\\). Using the identity \\((x-y)^2=x^2-2xy+y^2\\), take \\(x=2a\\) and \\(y=b\\). Then \\(x^2=4a^2\\), \\(2xy=2(2a)(b)=4ab\\), and \\(y^2=b^2\\). Hence the expansion is \\(4a^2-4ab+b^2\\).
The middle term is negative because the binomial contains subtraction. Its coefficient is 4, not 2, because the two equal cross-rectangles together contribute \\(2(2a)(b)=4ab\\). Therefore, option A is correct. Option D would apply to \\((2a+b)^2\\), while the other expressions do not follow the square identity.
Frequently asked questions
What is the correct answer to this question?
(4a^2-4ab+b^2)
Why is this the correct answer?
The area of a square is the square of its side. For side \\(2a-b\\), the area is \\((2a-b)^2\\). Using the identity \\((x-y)^2=x^2-2xy+y^2\\), take \\(x=2a\\) and \\(y=b\\). Then \\(x^2=4a^2\\), \\(2xy=2(2a)(b)=4ab\\), and \\(y^2=b^2\\). Hence the expansion is \\(4a^2-4ab+b^2\\).
The middle term is negative because the binomial contains subtraction. Its coefficient is 4, not 2, because the two equal cross-rectangles together contribute \\(2(2a)(b)=4ab\\). Therefore, option A is correct. Option D would apply to \\((2a+b)^2\\), while the other expressions do not follow the square identity.
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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