In Class 8, algebra becomes more advanced than in previous classes. In basic concepts of algebra for Class 8, we will discuss key terms, algebraic expressions, equations, and formulas with examples. These examples will be solved step by step.
Basic Concepts of Algebra for Class 8
We have discussed many basic terms of algebra in Class 6 and Class 7, like variables, constants, coefficients, and like and unlike terms. Now we will talk about terms.
Terms
A term is a single part of an algebraic expression separated by a plus (+) or minus (−) sign.
For example
2x + 5y – 4
Here, 2x, 5y, and -4 are the terms.
Algebraic Expressions with Types and Examples
If you want to read out the full article on algebraic expressions and their types, you can visit algebraic expressions.
Examples Related to Types
Monomial: 2x
Binomial: 2x -2
Trinomial: 4x + 2y – 6
Polynomial: 4x + 2y – 3z + 7
Algebraic Equations with Types and Examples
The following are examples related to every type of algebraic equation. For more details on this topic, check algebraic equations on our site.
Linear Equation
Q1. 2x + 6 = 8
Sol:
2x + 6 = 8
2x = 8 – 6
2x = 2
x = 1
Q2. 5x – 15 = 2x
Sol:
5x – 2x = 15
3x = 15
x = 15 / 3
x = 5
Quadratic Equation
Q3. 2x2 = 8
Sol:
2x2 = 8
x2 = 8 /2
x2 = 4
By taking the square root of both sides
x = ± 2
Q4. 3x2 – 2 = 25
Sol:
3x2 – 2 = 25
3x2 = 25 + 2
3x2 = 27
x2 = 27 / 3
x2 = 9
x = ± 3
Polynomial Equation
Q5. x3 – 4 = 60
Sol:
x3 – 4 = 60
x3 = 60 + 4
x3 = 64
Taking the cube root of both sides
x = 4
Algebraic Identities
Here are some examples related to every type of algebraic formula. To learn about algebraic formulas in detail, you can visit our guide to algebraic formulas and identities.
(a + b)2 = a2 + 2ab + b2
Q1. Find (x + 2)2
Sol:
(a + b)2 = a2 + 2ab + b2
(x + 2)2 = x2 + 2(x)(2) +22
= x2 + 4x + 4
Q2. Find (2x + 5)2
Sol:
(a + b)2 = a2 + 2ab + b2
(2x + 5)2 =( 2x)2 + 2(2x)(5) +52
= 4x2 + 20x + 25
(a – b)2 = a2 – 2ab + b2
Q3. Find (x – 2)2
Sol:
(a – b)2 = a2 – 2ab + b2
(x – 2)2 = x2 – 2(x)(2) +22
= x2 – 4x + 4
Q4. Find (2x – 5)2
Sol:
(a – b)2 = a2 – 2ab + b2
(2x – 5)2 =( 2x)2 – 2(2x)(5) +52
= 4x2 – 20x + 25
a2 – b2 = (a + b) (a – b)
Q5. Find (x + 5) ( x – 5)
Sol:
a2 – b2 = (a + b) (a – b)
x2 – 25 = (x + 5) ( x – 5)
Real-Life Applications of Algebra in Class 8
- Shopping discounts
- Mobile recharge plans
- Cricket run rate
- Distance and speed
- School marks
- Electricity bills
Algebra Vocabulary Table
| Word | Meaning | Example |
| Variable | Unknown value | x |
| Constant | Fixed value | 5 |
| Coefficient | Number before variable | 8x |
| Expression | No equal sign | 3x+2 |
| Equation | Has an equal sign | 3x+2=11 |
| Identity | Always true | (a+b)² = a² + 2ab + b² |
Common Algebra Symbols
| Symbol | Meaning |
| + | Addition |
| − | Subtraction |
| × | Multiplication |
| ÷ | Division |
| = | Equal |
| ≠ | Not Equal |
| > | Greater than |
| < | Less than |
FAQs
1. What exactly is the basic concept of algebra for Class 8?
The basic concepts of algebra for Class 8 include variables, constants, coefficients, terms, algebraic expressions, algebraic identities, and simple linear equations.
2. What does it mean to “solve” an equation?
The quick way to solve an equation is to find the value of the variable and apply various operations to both sides.
For example:
x + 5 = 12
Subtract 5 from both sides → x = 7
3. What’s a variable? And why does it keep changing?
A variable is a letter whose exact value is not known. It provides different values in every problem.
4. Is algebra supposed to be hard?
That’s completely normal. Algebra might feel challenging at first because it offers a new way of thinking.
5. Can you provide a quick example to try?
Sure! Try solving this:
3x + 4 = 19
Conclsuion
The basic concepts of algebra for class 8 cover algebraic equations, expressions, identities, and their examples related to every type. It also covers an overview of the key terms of algebra for class 8. After this topic, algebra for class 8 becomes easy, and it is also helpful for higher mathematics.
