What is the simplified form of ( (a+b+c)^2-(a^2+b^2+c^2+2ab) )?
Answer and explanation
Correct answer: (2bc+2ca)
Use the expansion of a square of three terms: \\( (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\\). The expression subtracts \(a^2+b^2+c^2+2ab\) from this complete expansion. The three square terms cancel, and the \(2ab\) term also cancels.
The terms left are \(2bc+2ca\), so option A is correct. It is useful to keep the subtraction bracket together; every term inside it is removed from the expanded square. Option B incorrectly retains \(2ab\), option C omits the \(2bc\) term, and option D omits the \(2ca\) term. The answer does not require assigning numerical values to the variables.
Frequently asked questions
What is the correct answer to this question?
(2bc+2ca)
Why is this the correct answer?
Use the expansion of a square of three terms: \\( (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\\). The expression subtracts \(a^2+b^2+c^2+2ab\) from this complete expansion. The three square terms cancel, and the \(2ab\) term also cancels.
The terms left are \(2bc+2ca\), so option A is correct. It is useful to keep the subtraction bracket together; every term inside it is removed from the expanded square. Option B incorrectly retains \(2ab\), option C omits the \(2bc\) term, and option D omits the \(2ca\) term. The answer does not require assigning numerical values to the variables.
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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