What are the square terms in \( (x+y+z)^2 \)?
Answer and explanation
Correct answer: \(x^2\), \(y^2\), \(z^2\)
A square term is produced when a quantity is multiplied by itself. In the expression \\( (x+y+z)^2 \\), the individual quantities are squared, giving \\(x^2\\), \\(y^2\\), and \\(z^2\\). These are called the square terms. When the expression is expanded, it also contains the mixed products \\(2xy\\), \\(2yz\\), and \\(2zx\\), but those are not square terms because they involve two different variables.
The identity is \\( (x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx\\). Thus option B lists exactly the three terms in which each variable is squared. Option A lists unsquared products, option C lists doubled cross-products, and option D is the original sum rather than a list of terms. The distinction is based on the exponent and the variables present.
Frequently asked questions
What is the correct answer to this question?
\(x^2\), \(y^2\), \(z^2\)
Why is this the correct answer?
A square term is produced when a quantity is multiplied by itself. In the expression \\( (x+y+z)^2 \\), the individual quantities are squared, giving \\(x^2\\), \\(y^2\\), and \\(z^2\\). These are called the square terms. When the expression is expanded, it also contains the mixed products \\(2xy\\), \\(2yz\\), and \\(2zx\\), but those are not square terms because they involve two different variables.
The identity is \\( (x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx\\). Thus option B lists exactly the three terms in which each variable is squared. Option A lists unsquared products, option C lists doubled cross-products, and option D is the original sum rather than a list of terms. The distinction is based on the exponent and the variables present.
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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