Question

Find the degree of the given algebraic expression $xy + yz$.

Answer 1

Hint – In this question manipulate the given algebraic expression by taking y common and then apply the basic rule degree of algebraic expression which states that degree is dependent upon the power of variable and also upon the variable multiplication.

Complete step-by-step answer:
Given algebraic expression
$xy + yz$
Now this expression is written as
$ \Rightarrow xy + yz = y\left( {x + z} \right)$
Now as we know degree of algebraic expression is dependent on the power of variable and it is also dependent on the variable multiplication but it is not dependent on the variable addition but it is dependent on highest power of the variable so in addition if first term has highest power and second term has lowest power than highest power of variable is a valid case.
So in the given equation all variables have equal power which is 1.
So it is independent in addition.
But two variable are multiplied together so the degree of algebraic expression is
Power of x + power of y (or) power of y + power of z.
So degree of algebraic expression = (1 + 1) = 2.
So this is the required answer.

Note – In simple words the degree of a polynomial with more than 2 variables is the sum of the exponents in each term and the degree of polynomial is the largest such sum. However in case of a single variable it is simply the highest power corresponding to that variable in the equation.