Question

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

Answer 1

Hint: First we’ll understand the degree of expressions with single and multiple variables.
Then we’ll find the degree of each term of the given expression and using that we’ll determine the degree of the whole expression.

Complete step by step solution: Given data: $pq + {p^2}q - {p^2}{q^2}$

The degree is the polynomial in one variable is the highest exponent of the variable in that polynomial, similarly, the degree of terms of a polynomial with one variable is the exponent of that variable in that term of the polynomial.

Similarly, the degree of a term of the polynomial with multiple variables is the summation of the exponents of all variables in that term and the highest degree on comparing the degree of all terms of that polynomial is the degree of that polynomial.

The degree of $pq$ (p has exponent 1 and q has exponent 1) $ = 2$

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

The degree of ${p^2}{q^2}$ (p has exponent 2 and q has exponent 2) $ = 4$

Therefore the degree of the expression is 4.

Note: Some of the students multiply the exponent of the multiple variable terms as the base are also in multiplication, avoid doing these kinds of mistakes as these exponents get added not multiplied.