What is Factorization Formula? with Examples

Factorization Formula: Factorization means breaking a number or expression into smaller parts called factors. When these factors are multiplied together, they give the original number or expression. The factorization method helps us to write numbers or algebraic expressions in a simpler way by finding their factors.

Using factorization formula, especially in class 8, students can solve many math problems easily. So to learn more about "what is factorization," along with its definition and examples, keep reading.

Read More: Division of Fractions

Factorization Definition Overview

To understand the formulas, it's important for students to first know the answer to the commonly asked question, "what is factorization?" In maths, factorization means breaking a number into smaller numbers, which are known as factors. When we multiply these factors, we get the original number back. 

For example, 14 can be broken into 7 × 2. Here, 7 and 2 are the factors of 14. This is the basic factorization definition in mathematics.

Read More: 30 Fun Maths Questions with Answers

What is Factorization Formula?

In maths, the factorization formula is used to split a number or an algebraic expression into simpler factors. These factors are smaller values or expressions that, when multiplied together, form the original number or expression. The factorization formula is generally written as:

N = Xᵃ × Yᵇ × Zᶜ

Where:

• N is the number or expression we want to factorize.

• X, Y, and Z are the factors.

• a, b, and c are the powers (also called exponents) of each factor.

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Here the factors can be:

• Regular numbers (like 2, 3, 5)

• Variables (like x, y)

• Algebraic expressions (like x + 2)

Using the factorization method, students can also solve algebraic expressions by writing them as a multiplication of two or more expressions instead of expanding brackets. This method makes it easier to simplify and solve equations.

Also Read: Skip Counting

Factorisation Formulas for Class 8

To make algebraic expressions easier, students in Class 8 learn some important factorisation formulas. These formulas help break down big expressions into smaller and simpler factors. They are useful in solving equations and understanding algebra better. Find out some commonly used factorisation formulas for Class 8 here:

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ - b³ - 3ab(a - b)

• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

• a² - b² = (a + b)(a - b)

• a³ - b³ = (a - b)(a² + ab + b²)

• a³ + b³ = (a + b)(a² - ab + b²)

These factorization formulas are helpful while solving the exercises given in the NCERT books, especially in questions where students need to break expressions into smaller factors.

Also Read: Types of Line in Math

Applications of Factorization Method in Maths

Factorization method is very useful in maths as it helps in solving various types of questions more easily. Here are some common ways we use the factorization method:

1. Solving Equations: When we factor algebraic expressions, it becomes easier to solve equations and find the value of unknown variables.

2. Simplifying Expressions: Factorization helps break big expressions into smaller parts. This makes it easier to work with and understand the expression.

3. Prime Factorization: In number theory, we use prime factorization to write a number as a product of prime numbers. This helps us understand the number better and check its divisibility.

4. Simplifying Fractions: By canceling common factors in the numerator and denominator, we can make fractions smaller and easier to use.

5. Solving Quadratic Equations: The factorization method is used to find the roots (solutions) of quadratic equations in a simple way.

6. Polynomial Division: When dividing one polynomial by another, factorization makes the process easier and helps in finding the answer correctly.

Read More: Ratio and Proportion

Factorization Formula With Solved Examples

Find out the solved examples based on NCERT questions using the factorization formulas for Class 8 here:

Example 1: Factorise: 12x + 36

Solution:

Step 1: Find the common factor of both terms.

• 12x = 3 × 4 × x

• 36 = 3 × 4 × 3 = 12 × 3

Step 2: The common factor is 12.

Step 3: Take 12 outside the bracket: 12x + 36 = 12(x + 3)

Final Answer: 12(x + 3)

Read More: Division of Fractions

Example 2: Factorise: 22y – 33z

Solution:

Step 1: Find the common factor of both terms.

• 22y = 11 × 2 × y

• 33z = 11 × 3 × z

Step 2: The common factor is 11.

Step 3: Take 11 outside the bracket:
22y – 33z = 11(2y – 3z)

Final Answer: 11(2y – 3z)

Example 3: Factorise: 14pq + 35pqr

Solution:

Step 1: Find the common factor.

• 14pq = 7 × 2 × p × q

• 35pqr = 7 × 5 × p × q × r

Step 2: Common factors = 7 × p × q = 7pq

Step 3: Take 7pq outside the bracket: 14pq + 35pqr = 7pq(2 + 5r)

Final Answer: 7pq(2 + 5r).

Read More: How to Prepare for Math Olympiads with Mental Maths

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