What is 65 + 9393445345643 + 3?

The combination of different terms that are connected by mathematical operations such as addition, subtraction, etc. is known as an algebraic expression. When it is said that terms are involved in an algebraic expression, it means that those terms can either be a variable, a constant, or a combination of both variable and constant, where both are connected by the multiplication operator in order to be counted as a term.

Types of algebraic expressions

There are majorly four types of algebraic expressions based on the number of terms present in the expression. The four types are monomial expressions, binomial expressions, trinomial expressions, and polynomial expressions. Let’s learn about their definitions,

1. Monomial expressions: The expression containing only one non-zero term is called a monomial term. For instance, 2 is a monomial expression with just a constant present in it, 4ab⁴ is also a monomial expression with 1 constant and 2 variables present in it.
2. Binomial expressions: The expression containing two non-zero terms is called a binomial expression. For instance, p+q is a binomial expression with 2 variables present in it.
3. Trinomial expressions: The expression containing three non-zero terms is called a trinomial expression. For instance, -8p+q⁵ + 8r is a trinomial expression with 3 variables present in it.
4. Polynomial expressions: The expression containing two or more than two non-zero terms is called a polynomial expression. For instance, -12p+q⁵ is a polynomial expression with 3 variables present in it.

What is 65 + 9393445345643 + 3?

Solution:

Looking at them in terms of algebraic expressions, it can be observed that they are a monomial expression after simplifying, adding 3 constant terms will provide a constant term. 

= 65 + 9393445345643 + 3

= 9,393,445,345,711

Therefore, the final answer is a monomial expression containing a constant.

Now that this concept is clear in head. Let’s move on to understand some similarities and then some more complex calculations in algebraic expressions,

Similar problems

Question 1: What is 31 + 7845 + 2?

Solution:

Looking at them in terms of algebraic expressions, it can be observed that they are a monomial expression after simplifying, adding 3 constant terms will provide a constant term.

= 31 + 7845 + 2

= 7,878

Therefore, the final answer is a monomial expression containing a constant.

Question 2: What is 23 + 5 + 1009700?

Solution:

Looking at them in terms of algebraic expressions, it can be observed that they are a monomial expression after simplifying, adding 3 constant terms will provide a constant term.

= 23 + 5 + 1009700

= 1,009,728

Therefore, the final answer is a monomial expression containing a constant.

Question 3: Add the given algebraic expressions,

1. 2x² + 4y + 89
2. 51x² + 3xy + 78

Solution:

The most important thing to notice while adding two algebraic expressions is the similarities in terms, simply add the terms that are similar to each other. Here, x² is common, they can be added, the contents can be added, while y and xy are different terms, so they will be written directly.

= (2x² + 51x²) + 4y + 3xy + (89 + 78)

= 53x² + 3xy + 4y + 167

Therefore, the above expression is the polynomial obtained after addition.

Question 4: Add the given algebraic expressions,

1. 5p² + 200q + 80
2. 43p² + 4pq + 10

Solution:

The most important thing to notice while adding two algebraic expressions is the similarities in terms, simply add the terms that are similar to each other. Here, x2 is common, they can be added, the contents can be added, while y and xy are different terms, so they will be written directly.

= (5p² + 43p²) + 200q + 4pq + (80 + 10)

= 48p2 + 4pq + 200q + 90

Therefore, the above expression is the polynomial obtained after addition.

Question 5: Identify the type of polynomial,

1. 3
2. 4x²
3. 5pq + 5r³ + 9

Answer:

1. 3 is a monomial expression.
2. 4x² is a monomial expression with a constant and a variable.
3. 5pq + 5r³ + 9 is a trinomial expression.

Question 6: Identify the type of polynomial,

1. 90
2. 14xu²
3. 35yz + 9x³ + 1

Answer:

1. 90 is a monomial expression.
2. 14xu² is a monomial expression with a constant and a variable.
3. 35yz + 9x³ + 1 is a trinomial expression.