Mathematics Simplex: Factorizing Algebraic Expressions

Introduction

• Welcome by Trisha Maurice.
• Channel: Mathematics Simplex.
• Topic: Factorizing Algebraic Expressions.

Understanding Expressions

• Expression: Group of terms without an equal sign.
• Example: 5a² - 10a is an expression.

What is Factorization?

• Factorization: Process of factoring out the highest common factor (HCF).
• Objective: Factor out what is common by creating brackets.

Steps to Factorize Expressions

1. Identify Coefficients and Variables:

   • Example: For 5a² - 10a, coefficients are 5 and 10.
   • Find the HCF of coefficients.

2. Determine Highest Common Factor (HCF):

   • Coefficients: Find largest number that divides each coefficient without remainder.
   • Variables: Determine common variable factor.

3. Factorization Process:

   • Example 1: 5a² - 10a

     • HCF of 5 and 10 is 5.
     • Factor out 5: 5(a² - 2a).
     • Factorize a²: a² / a = a.
     • Result: 5a(a - 2).

   • Example 2: 5y + 15

     • No variable in 15, only numbers.
     • HCF of 5 and 15 is 5.
     • Result: 5(y + 3).
     • Verification: Expand to check correctness.

   • Example 3: 5x² - 30x

     • HCF of 5 and 30 is 5.
     • Factor out 5 and x: 5x(x - 6).

   • Example 4: -12x² - 3x

     • Consideration of negative signs.
     • HCF is -3x.
     • Result: -3x(4x + 1).

Important Concepts

• Expansion: Confirm factorization by expanding back to original expression.
• Negative Signs:
  • Factor out negative signs when both terms are negative.

Conclusion

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