Why will (2xy) appear in ( (x+2+y)^2 )?
Answer and explanation
Correct answer: Because the double product of the pair (x) and (y) appears
The square of three terms contains the square of each term and twice the product of every distinct pair. For the terms in \\(x+2+y\\), the pair consisting of \\(x\\) and \\(y\\) contributes \\(2xy\\). Other pairwise products also occur, such as \\(4x\\) and \\(4y\\), along with \\(x^2\\), \\(4\\), and \\(y^2\\).
Thus, option B is correct. The term \\(2xy\\) does not appear because x and y are square terms; it appears because their product is counted twice when the whole sum is multiplied by itself. The number 2 does not disappear, and the expansion definitely contains product terms. Pairing the three terms prevents omissions.
Frequently asked questions
What is the correct answer to this question?
Because the double product of the pair (x) and (y) appears
Why is this the correct answer?
The square of three terms contains the square of each term and twice the product of every distinct pair. For the terms in \\(x+2+y\\), the pair consisting of \\(x\\) and \\(y\\) contributes \\(2xy\\). Other pairwise products also occur, such as \\(4x\\) and \\(4y\\), along with \\(x^2\\), \\(4\\), and \\(y^2\\).
Thus, option B is correct. The term \\(2xy\\) does not appear because x and y are square terms; it appears because their product is counted twice when the whole sum is multiplied by itself. The number 2 does not disappear, and the expansion definitely contains product terms. Pairing the three terms prevents omissions.
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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