Algebraic Expression and Some Important Algebraic Identities

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The art of expressing numbers using letters or alphabets without specifying their actual values is known as an algebraic expression. The basics of algebra include how to express an unknown value using letters such as x, y, z, etc. These letters are known as variables. An algebraic expression can be represented by both variables and constants.

A constant is a value that remains the same constantly and never changes. Any value that is placed before and multiplied by a variable is a coefficient. For example, let us take an equation 5x+3 where, x is a variable whose value is not known to us, 5 is the coefficient of x, 3 is a constant value term that never changes and remains the same constantly. Let us now understand the algebra formula, various types of algebraic expressions, and some important algebraic identities.

Algebra Formula

The algebraic formulas are used to form the base/foundation of numerous topics of mathematics. There are various topics such as quadratic equations, polynomials, coordinate geometry, calculus, trigonometry, probability, etc. that extensively depend on the algebra formulas. An algebra formula is an equation, where mathematical and algebraic symbols are written. For example, (a+b) (a+b)is an algebraic formula. Similarly, there are other algebra formulas as well.

Types of Algebraic Expressions

There are basically three types of algebraic expressions which are as follows:

1. Monomial expression: Any algebraic expression which has only one term is known as a monomial expression. For example, 3y, 3x, 8y, 9x, etc.

2. Binomial expression: Any algebraic expression which has two terms is known as binomial expression. For example, 5xy+8, x + 5z, 5x + 9, etc.

3. Polynomial expression: An expression with more than one term and non-negative integral exponents of a variable is known as polynomial expression.

For example, ax + by + ca, 2x + 3y + 1z, 5x + 6y – 7, etc.

Various Other Types of Algebraic Expressions

Other than monomial, binomial, and polynomial types of expressions, an algebraic expression can also be classified into other additional types which are as follows:

Numeric Expression

A numeric expression never includes a variable but consists of numbers and operations. Some of the examples of numeric expressions are 1 + 6, 35 ÷ 2, etc.

Variable Expression

A variable expression is an expression that consists of variables along with numbers and operations to define an expression. A few examples of a variable expression are as follows: 2x + y, 4ab + 33, 5b + 6, 7z + 1, etc. If you want to learn more about algebraic expressions and algebra formulas in detail and in a fun and interesting way, visit Cuemath.

Some Important Terms

1. Variable: Generally, in mathematics a symbol that doesn’t have a fixed value is called a variable. It can be of any value. Some examples of variables are as follows a, b, x, y, z, m, etc.

2. Constant: The opposite of a variable is a constant. A constant is a symbol that has a fixed value. Some examples of constants are as follows: 3, 4, 5, -1/2 etc.

3. Terms: A term is basically a constant or a variable that can be combined to get an operation of addition, multiplication, and so on. Some examples of terms are as follows: 3x.x, 4xy.y, etc.

4. Coefficients: The numbers that are multiplying the variables are known as coefficients. For example: 3, -2/3, 5, etc.

Some Algebraic Identities

Algebraic identity basically signifies that the left-hand side is equal to the right-hand side of a given equation. It is usually used to solve the values of unknown variables.

  • (a + b) (a+b) = a.a + 2ab + b.b
  • (a – b) (a – b) = a.a – 2ab + b.b
  • (a + b) (a – b) = a.a – b.b
  • (x + a) (x +b) = x.x + (a + b) x + ab

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