Question

Find the degree of the given algebraic expression $pq+p^{2}q-p^2{q}^2$.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

We know that the degree is the term with the greatest exponent and,

To find the degree of a monomial with more than one variable for the same term, just add the exponents for each variable to get the degree.

The given algebraic expression $pq+p^{2}q-p^2{q}^2$ has three terms. The first one is $pq$, the second is $p^{2}q$ and the third one is $-p^2{q}^2$.

$pq$ has degree $2$ ($p$ has an exponent of $1$, $q$ also has $1$, and $1+1=2$)

$p^{2}q$ has degree $3$ ($p$ has an exponent of $2$, $q$ has $1$, and $2+1=3$)

$p^2{q}^2$has degree $4$ ($p$ has an exponent of $2$, $q$ also has $2$, and $2+2=4$)

Since the highest degree amongst all the terms is $4$, therefore, the degree of $pq+p^{2}q-p^2{q}^2$ is $4$.

Hence, the degree of the algebraic expression $pq+p^{2}q-p^2{q}^2$ is $4$.