Algebra formulas are vital for students to learn and understand. It helps them in solving difficult mathematics problems. Well, algebra is a field of mathematics. That is why students have to learn algebra during their school time. It enhances students’ skills to solve mathematics problems efficiently.
But, for this, students must have a basic knowledge of algebra and its formulas. Moreover This helps you to get good grades in your academics. It is a vital concept for every student to learn and understand. Especially for those who want to achieve 90+ in their exam or assessment.
So, to understand this essential concept, keep reading this blog. Here, you will get the ultimate guide to algebraic formulas and algebra homework help. Therefore, are you ready? So, let’s get started.
Algebra Formula
Algebra is a branch of mathematics. Meanwhile it helps students solve mathematics problems and calculate unknown numbers. For example, variable values, constants, and percentages. Moreover, algebra helps in identifying a situation, when both fixed and dynamic components are present at the same time.
In addition, there are different branches of algebra in an algebra formula chart. For example:
- Elementary Algebra
- Advanced Algebra
- Abstract Algebra
- Linear Algebra
- Commutative Algebra
Basic Algebra
The following terms are important to basic algebra skills.
Exponent
It is the process of expressing huge numbers in terms of power. And it shows how many times a number has been multiplied by itself. For example, if 6 is multiplied by itself four times, resulting in 6 6 6 6 6. The exponent is 4 and the base is 6. This can be read as 6 multiplied by four.
Expression
An algebraic expression is at least one variable and one operation. That is addition, subtraction, multiplication, and division. For example, 2(x + 6y) is an algebraic expression.
Polynomials
A polynomial is made up of one or more algebraic terms. Each of them includes a fixed multiplied by one or more variables raised to a non-negative integral power. For example, a + bx + cx^2.
Basic Algebra Rules
The following are the basic algebra rules:
- The Symmetry Rule
- Two Rules Of Equation
- Commutative Rules
- The Inverse of Adding
Basic Algebra Operations
In the case of algebra, the following are the basic arithmetic operations:
- Addition: x + y
- Subtraction: x – y
- Multiplication: xy
- Division: x / y
where x and y are the variables.
The operations follow the BODMAS rule. So, It means that the terms inside the brackets will be considered first. And then comes roots and exponents. Therefore, solve all the division, multiplication, and finally addition and subtraction problems.
Basic Algebra Formulas
In mathematics, there are some basic formulas of algebra. Then there are four algebraic identities to examine, which are fixed equations that are true in all situations. So, firstly, let’s learn algebra identities.
- (a + b)^2 = a^2 + b^2 + 2 x a x b
- (a – b)^2 = a^2 + b^2 – 2ab
- (a + b) (a – b) = a^2 – b^2
- (x + a) (x + b) = x^2 + 2(a + b) + ab
Moving further, let’s now learn some basic algebra formulas. And these formulas have three variables with exponents that vary from one to three.
- (a + b )^2 = a^2 + b^2 + 2ab
- (a – b)^2 = a^2 + b^2 – 2ab
- (a + b) (a – b) = a^2 – b^2
- (a + b)^3 = a^3 + 3ab (a + b) + b^3
- (a – b)^3 = a^3 – 3ab (a – b) – b^3
- a^3 + b^3 = (a + b) (a^2 + ab + b^2)
- a^3 – b^3 = (a – b) (a^2 + ab + b^2)
- (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac
Now, let’s learn with the help of some examples.
Sample Problems
Example 1: Find the value of y, when y + 12 = 20
Solution: y + 12 = 20
Y = 20 – 12
Y = 8
Example 2: Find the value of x, when x – 6 = 10
Solution: x – 6 = 10
X = 10 + 6
X = 16
Example 3: Find the value of x, when 5x = 45
Solution: 5x = 45
X = 45/5
X = 9
Example 4: Find the value of y, when y/3 = 36.
Solution: y/3 = 36
Y = 36 x 3
Y = 108
Example 5: Solve the equation, 2y – 8 = 5y
Solution: 2y – 8 = 5y
-8 = 5y – 2y
-8 = 3y
-8/3 = y
Example 6: Find the value of Z, if 21z + 3 = 10
Solution: 21z + 3 = 10
21z = 10 – 3
21z = 7
Z = 7/21
Z = 1/3
Example 7: Find out the value of (2 + 3)^2, using algebraic formula.
Solution: Using an algebraic formula,
(a + b)^2 = a^2 + b^2 + 2ab
(2 + 3)^2 = 2^2 + 3^2 + 2 x 2 x 3
(2 + 3)^2 = 4 + 9 + 12
(2 + 3)^2 = 25
Final Words
To sum up, we have discussed the basic algebra formulas in the above blog. The above formulas are for beginners, who are new to this concept. Moreover, we have discussed all the essential information that a novice needs to know. Also, we have provided some examples as well to give an idea of how students can solve it. Therefore, in the end, we hope this blog will be helpful for you. To become an expert in algebra you need to do as much as practice you can.
