Question

Find the degree of the given algebraic expression.
$2{y^2}z + 9yz - 7z - 11{x^2}{y^2}$
(A)$2$
(B) $3$
(C) $4$
(D) \[5\]

Answer 1

Hint: Before dealing with the question we need to focus on the same term:-
Algebraic expression: \[ - An\] algebraic expression is a mathematical expression that consists of variables, numbers and operations (addition, subtraction, multiplication and division).


Complete step by step solution:
$2x + 3yz$ is an algebraic expression.
Term of the algebraic expression: - An algebraic expression is made up of the terms (separated by addition and subtraction). The term of algebraic expression $2x + 3yz$ is $2x,3yz$.
Power of the term of the algebraic expression: - In a term, the sum of exponents of the variable represents its power. For example, the power of the term of $2x = 2{x^1}$ is \[1\] and $3yz = 2{y^1}{z^1}$ is\[2\] .
Degree of algebraic expression:- The highest power in the algebraic expression represents its degree.
Let just take the same example where power of the term of $2x = 2{x^1}$ is \[1\] and $3yz = 2{y^1}{z^1}$ is \[2\] So the degree of $2x + 3yz$ is \[2\].
Since now we are aware of all the definition, let’s take us to look at our question,
$2{y^2}z + 9yz - 7z - 11{x^2}{y^2}$
Terms of this algebraic expression will be,
$2{y^2}z,9yz, - 7z, - 11{x^2}{y^2}$
Power of $2{y^2}z$ is \[3\] .
Power of $9yz$is \[2\].
Power of $ - 7z$is \[1\] .
Power of $ - 11{x^2}{y^2}$ is \[4\] .
Now we can easily infer the degree of given algebraic expression which is \[4\].
Thus, the degree of algebraic expression $2{y^2}z + 9yz - 7z - 11{x^2}{y^2}$ is \[4\].
Therefore the correct option is \[C\] which is \[4\] .


Note: Here,students must know the definition of power and degree as it is interrelated terms. Power is of the term whereas degree is of complete algebraic expression.