Simplify ( (a+b+c)^2-(a^2+b^2+c^2+2ab) ).
Answer and explanation
Correct answer: (2bc+2ca)
Expand the square of three terms using \\(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\\). Substituting the given terms, the first expression becomes \\(a^2+b^2+c^2+2ab+2bc+2ca\\). Now subtract \\(a^2+b^2+c^2+2ab\\). These four terms cancel exactly, leaving only the two cross-products \\(2bc+2ca\\).
Thus option A is correct. The term \\(2ab\\) is removed because it appears in the quantity being subtracted, and \\(abc\\) cannot appear because squaring a sum produces squared terms and pairwise products, not a product of all three variables. The result may also be written as \\(2c(a+b)\\), which is algebraically equivalent to \\(2bc+2ca\\).
Frequently asked questions
What is the correct answer to this question?
(2bc+2ca)
Why is this the correct answer?
Expand the square of three terms using \\(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\\). Substituting the given terms, the first expression becomes \\(a^2+b^2+c^2+2ab+2bc+2ca\\). Now subtract \\(a^2+b^2+c^2+2ab\\). These four terms cancel exactly, leaving only the two cross-products \\(2bc+2ca\\).
Thus option A is correct. The term \\(2ab\\) is removed because it appears in the quantity being subtracted, and \\(abc\\) cannot appear because squaring a sum produces squared terms and pairwise products, not a product of all three variables. The result may also be written as \\(2c(a+b)\\), which is algebraically equivalent to \\(2bc+2ca\\).
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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