Question

Find the degree of the given algebraic expression \[xy+yz\]?

Answer 1

Hint: We are given a question with an algebraic expression and we have to find the degree of this given algebraic expression. Degree of an algebraic expression refers to the maximum power raised to in a term within the given expression. In the given expression we can see that there are three variables ‘x’, ‘y’ and ‘z’. in the first term, which is \[xy\], we have the degree of ‘x’ as 1 and the degree of ‘y’ as 1 too, so as a term the degree is 2. Next, we have the term \[yz\]. We can see that the degree of ‘y’ is 1 and the degree of ‘z’ is 1 and so the degree of this term also comes out to be 2. Hence, we have the value of the degree of the given algebraic expression.

Complete step by step solution:
According to the given question, we are given an algebraic expression whose degree we have to find.
Degree of an algebraic expression refers to the maximum power raised to a term in that expression.
The expression that we have is,
\[xy+yz\]
If we observe the given expression, we can see that the expression has three variables namely ‘x’, ‘y’ and ‘z’.
The first term that we have is, \[xy\]. In this term, we have the variables ‘x’ and ‘y’. Here, the degree of ‘x’ is 1 and the degree of ‘y’ is 1. So, the degree of the term comes out to be the sum of the degree of the components in the term, that is, 2.
Next, we have the term \[yz\]. In this term, we have the variables ‘y’ and ‘z’. Here, the degree of ‘y’ is 1 and the degree of ‘z’ is 1. So, the degree of this term comes out to be the sum of the degrees of the constituents, that is, 2.
Since, the maximum degree that we have is 2.

Therefore, the degree of the given algebraic expression is 2.

Note: Most of the mistakes occur when we forget to add up the degree of the components of a term. Like in the case of \[yz\], ‘y’ has the degree 1 and ‘z’ has the degree 1, but the degree of the term is not 1 rather it is \[1+1=2\], which is the sum of the degrees of the constituents of a term.