Algebra Calculator

This algebra calculator is used to solve algebraic expressions and equations. No need to sign up or get registered, simply input your algebra problems, scan, copy-paste, or upload an image of that question to get an instant solution.

By using this free algebra equation solver, you can solve various questions including:

Simplifying algebraic expressions
Performing operations on algebraic terms
Solving linear & quadratic equations
Factoring polynomials
Expanding and evaluating expressions
Finding roots of equations
Solving systems of equations
Working with inequalities
Finding function values

What is Algebra?

The term "algebra" comes from the Arabic word "al-jabr", meaning "reunion of broken parts." Persian mathematician Al-Khwarizmi is known as the "father of algebra." It is defined as:

Algebra is a branch of mathematics uses alphabetical letters and symbols to find unknown numbers and solve equations. These symbols and letters (x, y, and z) are called variables.

How To Use This Algebra Solver?

Type the equation, paste it, or upload an image
Click on "Calculate" to get instant solution

Our online Algebra Calculator provides you step-by-step solution, allowing you to use it again and solve as many questions as you want.

How To Solve Algebraic Expressions?

To solve algebraic expressions, follow the steps below:

Read the question & understand the equation
Combine like terms
Move the variable to one side and the constants to the other
Perform arithmetic to find the variable's value

Operations With Algebraic Terms:

Addition of Algebraic Terms:

To add expressions, we must have like terms. Like terms are terms that contain the same variable or group of variables raised to the same exponent, regardless of their numerical coefficient.

Example:

3x + 5x = 8x
2a + 4b + 3a = 5a + 4b

Subtraction of Algebraic Terms:

Subtraction of the algebraic terms are the similar to addition. It also applies only to the like terms. Subtract the coefficients of like terms while keeping the variable and its power unchanged.

Example:

7y - 3y = 4y
6m - 2n - 4m = 2m - 2n

Multiplying of Algebraic Terms:

When multiplying algebraic terms, multiply the coefficients together and then apply the laws of exponents to the variables. If the variables are the same, add their exponents manually or get help of this algebra calculator.

Example:

(3x)(4x) = 12x²
(2a)(3b) = 6ab

Division of Algebraic Terms:

When dividing algebraic terms, divide the coefficients and subtract the exponents of like variables. If the variables are different, they remain unchanged.

Example:

6x³ / 3x = 2x²
10ab / 5a = 2b

How Do You Solve Basic Algebraic Equations?

✔️ One-Step Algebraic Equations

Addition or Subtraction Equations

Solve x + 3 = 5
Subtract 3 from both sides: x = 5 - 3
x = 2

Multiplication or Division Equations

Solve x/3 = 7
Multiply both sides by 3: x = 7 * 3
x = 21

✔️ Two-Steps Algebraic Equations

Solve 3x + 5 = 14
Subtract 5 to both sides: 3x = 9
Divide both sides by 3 : x = 3

✔️ Multi-Steps Algebraic Equations

Solve the equation: 2(x + 3) - 5 = 7
Clear parentheses: 2x + 6 - 5 = 7
Combine like terms: 2x + 1 = 7
Subtract 1 from both sides: 2x = 7 - 1 = 6
Divide 2 on both sides: x = 3

✔️ Equations with Variables on Both Sides

Solve 2x + 3 = x + 9
Combine like terms: 2x - x = 9 - 3
Simplify: x = 6

FAQs:

What is the Difference Between an Expression and an Equation?

An expression is a combination of numbers, variables, and mathematical operations and does not contain an equal sign.

E.g: 3x + 5, 2x - y

An equation is a combination of two expressions along with the equal sign.

E.g: 2x + 5 = 11, x² - 4x + 3 = 0

How Do You Solve Linear Equations?

2x + 5 = 15

Subtract 5 on both sides: 2x = 10

Divided by 2: x = 5

What is the Quadratic Formula and How is it Used?

2x^2 - 4x - 6 = 0

Use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

Here: a = 2, b = -4, and c = -6

b² - 4ac = (-4)² - 4(2)(-6) = 16 + 48 = 64

(-(-4) ± √64) / (2(2)) = (4 ± 8) / 4

x = 3 , x = -1

Is this Algebra Equation Solver free to use?

Yes, this algebraic expression calculator is free and accessible to anyone for solving various algebraic problems.

What are the 5 basic rules of algebra?

Commutative Property
Associative Property
Distributive Property
Identity Property
Inverse Property

What are some important algebraic formulas?

a² – b² = (a-b)(a+b)
(a+b)² = a² + 2ab + b²
(a-b)² = a² – 2ab + b²
a² + b² = (a-b)² +2ab
(a+b+c)² = a²+b²+c²+2ab+2ac+2bc
(a-b-c)² = a²+b²+c²-2ab-2ac+2bc
a³-b³ = (a-b) (a² + ab + b²)
a³+b³ = (a+b) (a² – ab + b²)
(a+b)³ = a³+ 3a²b + 3ab² + b³
(a-b)³ = a³- 3a²b + 3ab² – b³

How Do You Solve Equation Using Substitution?

You can use free algebra calculator for a quick solution or if you want to find it manually then have a solution below:

Equation # 1: x + y = 10
Equation # 2: 2x - y = 4

Solution:

From the first equation, we can get: y = 10 - x

Substitute ‘y’ in the second equation:

2x - (10 - x) = 4

2x - 10 + x = 4

3x = 4 + 10

3x = 14

x = 14 / 3

To find the value of ‘y’ we put x in the first equation:

y = 10 - 14/3

y = 30 / 3 - 14 / 3

y = 16 / 3

So, x = 14 / 3 , y = 16 / 3

References:

Khan Academy: Algebra, Solving equations and inequalities, Linear equations and graphs.

Lumen Learning: Algebra, Algebraic operations on functions