What is the value of ((x+y)^2-(x-y)^2-4xy)?
Answer and explanation
Correct answer: 0
The governing concept is the pair of square identities: (x+y)^2=x^2+2xy+y^2 and (x-y)^2=x^2-2xy+y^2. Subtract the second expansion from the first. The x^2 and y^2 terms cancel, while 2xy-(-2xy)=4xy. The complete expression is therefore 4xy-4xy=0. Hence option A is correct. A common error is to stop after evaluating only the difference of the first two squared expressions; that gives 4xy, which is option B, but the original expression still contains the final subtraction of 4xy. Option C incorrectly treats the result as half of the intermediate term, and option D is not produced by subtracting these two square expansions. The cancellation must be completed before choosing the answer.
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What is the correct answer to this question?
0
Why is this the correct answer?
The governing concept is the pair of square identities: (x+y)^2=x^2+2xy+y^2 and (x-y)^2=x^2-2xy+y^2. Subtract the second expansion from the first. The x^2 and y^2 terms cancel, while 2xy-(-2xy)=4xy. The complete expression is therefore 4xy-4xy=0. Hence option A is correct. A common error is to stop after evaluating only the difference of the first two squared expressions; that gives 4xy, which is option B, but the original expression still contains the final subtraction of 4xy. Option C incorrectly treats the result as half of the intermediate term, and option D is not produced by subtracting these two square expansions. The cancellation must be completed before choosing the answer.
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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