What is the correct expansion of the identity ( (a+b)^2 )?
Answer and explanation
Correct answer: (a^2+2ab+b^2) / correct expansion
The square of a sum contains three parts: the square of the first term, twice the product of the two terms, and the square of the second term. In algebraic form, the identity is \\(a+b\\)^2=a^2+2ab+b^2. The middle term appears because the two cross-products, \(ab\) and \(ba\), are equal and together make \(2ab\).
Applying this identity gives the expansion \(a^2+2ab+b^2\), so option B is correct. For example, if both terms are added and the result is multiplied by itself, the products are \(a^2\), \(ab\), \(ba\), and \(b^2\). The two middle products combine to \(2ab\). Option A omits these products, while option C gives the wrong sign and option D is not a square expansion.
Frequently asked questions
What is the correct answer to this question?
(a^2+2ab+b^2) / correct expansion
Why is this the correct answer?
The square of a sum contains three parts: the square of the first term, twice the product of the two terms, and the square of the second term. In algebraic form, the identity is \\(a+b\\)^2=a^2+2ab+b^2. The middle term appears because the two cross-products, \(ab\) and \(ba\), are equal and together make \(2ab\).
Applying this identity gives the expansion \(a^2+2ab+b^2\), so option B is correct. For example, if both terms are added and the result is multiplied by itself, the products are \(a^2\), \(ab\), \(ba\), and \(b^2\). The two middle products combine to \(2ab\). Option A omits these products, while option C gives the wrong sign and option D is not a square expansion.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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