Question

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.
\[3{x^2}y{z^2} - 3x{y^2}z + {x^2}y{z^2} + 7{x^2}{y^2}z\]

Answer 1

Hint: Here we are asked to simplify the given algebraic expression and find whether the simplified expression is monomial, binomial, or trinomial. Simplifying the algebraic equation can be done by combining the like terms. Then we will check whether the simplified expression using the following:
Monomial – expressions having one terms
Binomial – expression having two terms
Trinomial – expressions having three terms

Complete step by step answer:
It is given that the algebraic equation is \[3{x^2}y{z^2} - 3x{y^2}z + {x^2}y{z^2} + 7{x^2}{y^2}z\]. We aim to simplify the given expression by combining the like terms and find whether it is a monomial, a binomial, or a trinomial.
Consider the given expression, \[3{x^2}y{z^2} - 3x{y^2}z + {x^2}y{z^2} + 7{x^2}{y^2}z\]
As we can see that the first term and the third are like terms, let's combine them.
\[4{x^2}y{z^2} - 3x{y^2}z + 7{x^2}{y^2}z\]
Now there are no like terms in the above expression so, we don’t need any further simplification.
Let us check whether the simplified expression is a monomial, a binomial, or a trinomial.
Consider the simplified expression, \[4{x^2}y{z^2} - 3x{y^2}z + 7{x^2}{y^2}z\] we can see that it contains three terms.
We know that the expression containing only three terms is called trinomial thus, this is a trinomial expression.
Therefore, the simplified given expression is \[4{x^2}y{z^2} - 3x{y^2}z + 7{x^2}{y^2}z\] and is a trinomial expression.

Note:
The like terms are nothing but the terms having the same variable. Like terms differ in their numerical coefficients. The terms that do not have the same variable factors are called, unlike terms. In general, an expression having one or more terms is known as a polynomial. In polynomials, a variable cannot appear in the denominator.