Do you want to know how to solve algebraic expressions step by step, in detail, for beginners? If you do, you’ve come to the right article.
Algebraic expressions come from the declaration of algebraic terms. In mathematics, an expression is a phrase composed of mathematical terms.
In this article, we will learn how to solve algebraic expressions step by step for beginners using 10 examples, as well as practice questions, for the ease of students. After reading this article, it will be easy for every school-going student to solve algebraic expressions easily.
This concept is not only for school but also in real life. It is helpful in budgeting, cooking, calculating travel times, and many other fields. Before solving the algebraic expressions, every student must know about the definition and the basic terms used in them.
What is an algebraic expression?
An algebraic expression is a combination of different algebraic terms.
For example
2x + 5 – 9
3y + 7 – 6
7y × 5
Do you notice that there is no equal sign in these examples? The main reason is that algebraic equations have an equal sign, not an algebraic expression.
Related Topics:
Algebraic Equations with answers
You can also visit algebraic expressions on Wikipedia.
Key Terms in Algebraic Expressions:
In the above section, we’ve discussed some algebraic terms. Here, we will talk through the basic components of algebraic expressions.
Variable: whose value is unknown, like x, y, z
Constant: Known value like 2, 3, 5
Coefficient: Constant term used at the start of a variable
Components of Algebraic Expressions in the Form of a Table:
| Expressions | Variables | Constants | Coefficients |
| 4x + 7 – 8 | x | 7, -8 | 4 |
| 2y – 7 | y | -7 | 2 |
| 3z + 8 – 1 | z | 8, -1 | 3 |
| 2a + b – 3c | a, b, c | 0 | 2, 1, -3 |
| x/2 | x | 0 | 1/2 |
If there is nothing with the variable, then the coefficient is 1.
Activity of Finding Key Terms through Examples
Here is a self-assessment for you to find the key terms of algebraic expressions from the examples given below, so that your concept becomes clear.
- 2x + 7 – 4
- 5x – 30
- 7x
- 5+ 7 – 3
- x/2 + x – 9
Types of Algebraic Expression with Examples:
The following are the types of algebraic expressions for beginners, so that students can understand how to solve algebraic expressions step by step for beginners easily.
- Monomial Expression:
The word mono means one. An expression in which only one term is used is called a monomial expression.
For example:
2x, 5y,
- Binomial Expression:
Here, bi means two. So, the expressions that contain two terms are called binomial expressions.
For example:
2x + 6
4y – 7
- Trinomial Expressions:
An expression having three terms is known as a trinomial expression.
For example:
4x + 3y – 7
2x2 + 3x + 1
- Polynomial Expression:
“An expression with one or more terms and non-negative integer powers of variables is called a polynomial expression.”
For example:
2x2 + 4x + 1
2x3 + 3x2 – 5x +1
How to Solve Algebraic Expressions Step by Step for Beginners:
Here are the 15 solved examples of algebraic expressions for beginners so that they can easily solve them step by step. This section is helpful for the class 6, 7, and 8 students. The BODMAS RULE is used in solving algebraic expressions easily.
Q1. Find 2x if x = 5
Solution:
2x = 2(5) = 10
Q2. Find 4x – 5y if x = 2 and y = 1
Solution:
4x – 5y = 4(2) – 5(1) = 8 – 5 = 3
Q3. Find 3x + 5y – 6z if x = 1 , y = 2, z = 3
Solution:
3x + 5y – 6z = 3(1) + 5(2) – 6(3) = 3 + 10 – 18
= 13 – 18 = -5
Q4. Simplify 4x – 2y + 2x + 6y
Solution:
=4x – 2y + 2x + 6y
= 4x + 2x – 2y + 6y
= 6x + 4y
Q5. Simplify x + y – z + 3x – 2z
Solution:
=x + y – z + 3x – 2z
=x +3x + y – z – 2z
=4x + y – 3z
Q6. Simplify [2x + 3y + {4x – (2y)}]
Solution:
=[2x + 3y + {4x – 2y}]
=[2x + 3y + 4x – 2y]
=6x + y
Q7. Solve [ 4y + { 2y – 5}]
Solution:
=[ 4y + { 2y – 5}]
=[4y + 2y – 5]
= 6y – 5
Q8. Solve 4a [14b ÷ 2b × 3]
Solution:
= 4a [14b ÷ 2b × 3]
= 4a [7b × 3]
=4a [21b]
=84ab
Q9. Simplify 16x + 2y [4x – 2y × 3]
Solution:
=16x + 2y [4x – 2y × 3]
=16x + 2y [4x – 6y]
=16x + 8xy – 12y2
Q10. Solve x2 + 2x + 1
Solution:
=x2 + 2x + 1
=(x + 1)2
Practice Questions:
Q1. Find 3x if x = 5
Q2. Find 4x + 6 if x = 2
Q3. Find 3x + 4y – 7 if x = 3, y = 2
Q4. 4x + 7y – 2 if x = y = 6
Q5. Solve [ 2x + y – { 3x – y }]
Q6. Simplify [ 3x + y – { 4x + y – (z)}]
Q7. Simplify 12a ÷ 3
Q8. Evaluate 3m − 2n if m=5, n=1
Q9. Find ( x + 2)2 if x = 4
Q10. Simplify ( x – 5)2
Answers:
1. 15
2. 14
3. 10
4. 64
5. -x + 2y
6. -x + z
7. 4a
8. 13
9. 36
10. x2 – 10x + 25
FAQ’s:
- What are common algebraic mistakes?
The common mistake that confuses every student while solving problems is the addition and substitution rules.
- What is the specialty in algebraic expressions?
There is no equal sign in algebraic expressions, and this makes it different from algebraic equations.
- How to solve algebraic expressions step by step for beginners?
The BODMAS rule occurs during problem-solving.
- How many variables are in an algebraic expression?
It is necessary to have a minimum one variable in an algebraic expression.
- What are the basic components of algebraic expressions?
The basic components are variables, constants, coefficients, and operators.
Conclusion:
This article analyzes how to solve algebraic expressions step by step for beginners in detail. After covering their components, their types, and solved examples, every student can have a strong grip on this topic.
