Using identity, what is the value of ( (x+y+z)^2 ) if (x=1), (y=2), (z=3)?
Answer and explanation
Correct answer: (36)
The expression \\(x+y+z)^2\\) means that the whole sum of the three numbers is multiplied by itself. An algebraic identity gives the same result in expanded form: \\(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx\\). The important point is that the square applies to the complete sum, not separately to only one term. Thus, the expression has one definite numerical value after the given values are substituted.
Substitute \\(x=1\\), \\(y=2\\), and \\(z=3\\). First find the sum: \\(x+y+z=1+2+3=6\\). Now square it: \\(6^2=36\\). The identity confirms this: \\(1^2+2^2+3^2+2(1)(2)+2(2)(3)+2(3)(1)=1+4+9+4+12+6=36\\). Therefore, option B is correct. Option A, 25, would result from an incorrect sum or operation.
Frequently asked questions
What is the correct answer to this question?
(36)
Why is this the correct answer?
The expression \\(x+y+z)^2\\) means that the whole sum of the three numbers is multiplied by itself. An algebraic identity gives the same result in expanded form: \\(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx\\). The important point is that the square applies to the complete sum, not separately to only one term. Thus, the expression has one definite numerical value after the given values are substituted.
Substitute \\(x=1\\), \\(y=2\\), and \\(z=3\\). First find the sum: \\(x+y+z=1+2+3=6\\). Now square it: \\(6^2=36\\). The identity confirms this: \\(1^2+2^2+3^2+2(1)(2)+2(2)(3)+2(3)(1)=1+4+9+4+12+6=36\\). Therefore, option B is correct. Option A, 25, would result from an incorrect sum or operation.
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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