Algebraic Expressions Formula

Algebraic Expressions Formula – Algebraic expressions are the concept of expressing numbers with letters or alphabets without stating their real values. The fundamentals of algebra taught us how to express an unknown value with letters such as x, y, and z. These letters are referred to as variables. An algebraic expression can consist of both variables and constants. A coefficient is defined as any value that comes before and is multiplied by another variable.

Algebraic Expressions Formula

In mathematics, an algebraic expression is one that combines variables and constants as well as algebraic operations (addition, subtraction, and so on). Expressions are composed of terms. Solve questions in Algebraic Expressions Worksheets at Extramark’s.

Examples –

6x + 2y – 4,  3x – 8, etc.

These expressions are represented using unknown variables, constants, and coefficients. The combination of these three terms is referred to as an expression. Algebraic expressions, unlike algebraic equations, do not have sides or equal sign.

Example: 3x + 5

• x is a variable, whose value is unknown to us which can take any value.
• 3 is known as the coefficient of x, as it is a constant value used with the variable term and is well defined.
• 5 is the constant value term that has a definite value.

The whole expression is known to be the Binomial term, as it has two unlikely terms.

Algebraic Expression Types

There are 3 main types of algebraic expressions which include:

• Monomial Expression – An algebraic expression which is having only one term is known as a monomial. Examples – 3x⁴, 3xy, 3x, 8y, etc.
• Binomial Expression – A binomial expression is an algebraic expression which is having two terms, which are unlike. Examples – 5xy + 8, xyz + x³, etc.
• Polynomial Expression – In general, an expression with more than one term with non-negative integral exponents of a variable is known as a polynomial. Examples – ax + by + ca,  x³ + 2x + 3, etc.

List of Algebraic Expression Formula

• 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
• (a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴
• (a – b)⁴ = a⁴ – 4a³b + 6a²b² – 4ab³ + b⁴
• a⁴ – b⁴ = (a – b)(a + b)(a² + b²)
• a⁵ – b⁵ = (a – b)(a⁴ + a³b + a²b² + ab³ + b⁴)
• “n” is a natural number, aⁿ – bⁿ = (a-b) (a^n-1 + a^n-2b +….b^n-2a + b^n-1)
• “n” is a even number, aⁿ + bⁿ = (a+b) (a^n-1 – a^n-2b +….+ b^n-2a – b^n-1)
• “n” is an odd number aⁿ + bⁿ = (a-b) (a^n-1 – a^n-2b +…. – b^n-2a + b^n-1)
• (a^m)(aⁿ) = a^m+n (ab)^m = a^mn

Algebraic Expressions Solved Examples

Example: Simplify the given expressions by combining the like terms and write the type of Algebraic expression.

(i) 5xy­­³ + 4x² y³ + 3y³x

(ii) 5ab² c² + 2a³ b² − 3abc – 5ab² c² – 2b² a³ + 2ab

(iii) 50x³ – 20x + 8x + 21x³ – 3x + 15x – 41x³

Solution:

Creating a table to find the solution:

Example 2: Find the value of 10² – 6²

Solution: Now these are simple numbers, so we can calculate the answer. But the correct method is to apply the formula,

a² – b² = (a-b)(a+b)

10² – 6² = (10-6)(10+6) = 4 × 16 = 64