Imagine you’re hosting a party for a number of people. And you are to cook food for them against the proportion given in the recipe book, how would you adjust the recipe for a different number of people? Here, you are going to need to change the ingredients accordingly to match the needed servings. So, how do you proceed? Well, it’s simple! Just use Algebra! But what is algebra? What constitutes it? What are its expressions? Let us study further and help you understand the different types of algebraic expressions and its parts.
What is Algebra?
One of the most important parts of mathematics is Algebra. You must have noticed sometimes, certain equations have alphabets attached to them where a person expected to calculate the value of the said alphabet. This form of the equation is algebra and these alphabets are the algebraic expressions and its parts. These expressions are used while writing word problems in mathematical terminologies. Algebraic expressions are useful in determining the value of the variable in any given equation. Learning algebra helps sharpen your deductive skills and is useful in more than just a mathematics class.
What Constitutes Algebraic Expressions?
There are several symbols and terms that collectively form- algebraic expressions and its part. These expressions are made up of integer constants, variables and the basic calculation tools such as addition, multiplication, subtraction, and division. Each of these operations are used in a specific way in every equation and there are certain laws one has to understand in order to accurately apply the formulas to an algebraic equation.
|7 is added to a number x||x+7|
|7 is deducted from a number y||y-7|
|7 is divided by a number b||7÷b|
|7 is multiplied by a number a||7×a|
These are expressions which include numbers along with operations, but they do not have variables. For example:
- 8 + 12 : Here, number 8 is added to 12.
- 2 × 9 – 3: Here number 2 is multiplied by 9 and the resultant is subtracted by 3
- 7 + 9 ÷ 6: Here the number 9 is divided by 6 and the resultant is added by 7.
These are definitely the most easiest form of algebraic expression since there are only constants in it. You’ll never find any variable in the numeric expressions, thereby adding to their simplicity.
These are expressions which also include variables along with numbers and operations. For example:
- 5a i.e. 5 times the variable a.
- 4x i.e. 4 times the variable x.
- 5x+4y i.e. 5 times the variable x and 4 times the variable y.
Here the values of the variable are unknown. So, by putting these variables into the equation, we are able to ascertain the value of this variable in numerical terms.
Let us now break down the parts of expressions for you. You need to first understand what are “terms” before you can better understand the algebraic expressions. Expressions are basically built up of terms. These terms may be understood as the end result of factors, which are either in numerical form, alphabetical or algebraic.
Terms are of two kinds
- Like Terms: Those terms which contain the same factors of algebra are called like terms.
- Unlike Terms: Those terms which contain different factors of algebra are called, unlike terms.
The numerical part of a term is called coefficient. At times, a part of the term or a factor may be called coefficient of remaining part of the term. For example:
- The expression x2 + x + 3 consists of three terms, i.e., x2, x and 3.
- The coefficient of each term is 3.
- In the expression 2a +5, 2 is the coefficient.
Now that we have understood what is a term and what are coefficients, let us now look at some other terms which are also parts of an algebraic expression.
- Monomial: This is algebraic expressions which has a single non-zero term. For example, b is a single variable monomial and 9 ab2 is a monomial with two variables a and b.
- Binomial: This is an algebraic expression which has two non-zero terms. For example, a+ b is a two variables binomial a and b, and x2 + 2y is two variables with single term binomial in x and y.
- Trinomial: An algebraic expression with three non-zero terms is referred to as trinomial. For example, a+b+c is trinomial with just three variables a, b and c, and 3x+2y+4a is a trinomial with three variables x,y and two terms.
- Polynomial: An algebraic expression with two or more terms is called polynomial. For example, 3a + 4b is a polynomial in two variables a and b, with two terms and 7xy + 4x + 2 is a polynomial in two variables x and y with three terms.
Solved Example For You
Q. In the expansion of (2x2−8) (x−4) 2, find the value of the coefficient of x3
Sol: A. -16
(2x2−8) (x−4) 2
=2x4 − 16x3 + 32x2 − 8x2+ 64x − 128
=2x4 − 16x3+ 24x2+ 64x − 128
Ans. Coefficient of x3 is −16