Factorization of algebraic expressions involves breaking down an expression into simpler factors, such that when multiplied together, they give the original expression. There are several techniques used in factorization depending on the type of algebraic expression.

Common Techniques of Factorization:

1. Factoring out the Greatest Common Factor (GCF): This is the simplest method where we factor out the largest common factor from all the terms of the expression. $ax + ay = a(x + y)$

2. Difference of Squares: This method is used for expressions of the form $a^2 - b^2$, which can be factored as: $a^2 - b^2 = (a - b)(a + b)$

3. Trinomials (Quadratic expressions): For a quadratic expression of the form $ax^2 + bx + c$, we look for two numbers whose product is $ac$ and whose sum is $b$, and then factor the expression accordingly. Example: $x^2 + 5x + 6 = (x + 2)(x + 3)$

4. Perfect Square Trinomials: This technique applies to expressions like $a^2 + 2ab + b^2$ or $a^2 - 2ab + b^2$, which can be factored as: $a^2 + 2ab + b^2 = (a + b)^2$ $a^2 - 2ab + b^2 = (a - b)^2$

5. Grouping: This method is useful when there are four or more terms. We group the terms in pairs and factor out the common factor from each group. Example: $ax + ay + bx + by = (a + b)(x + y)$

Would you like to see detailed examples or solutions to a specific type of factorization?

Related Questions:

1. How do you factor expressions involving multiple variables?
2. What are some examples of factoring cubic expressions?
3. How do you factor expressions involving fractional exponents?
4. Can all quadratic expressions be factored using integers?
5. What is the role of the discriminant in quadratic factorization?

Tip:

Always start by factoring out the greatest common factor (GCF) before using other methods.