1. Let's start by stating the problem: How to factor an algebraic expression. 2. Factoring means rewriting an expression as a product of simpler expressions. 3. The most common factoring formulas are: - Difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$ - Perfect square trinomial: $$a^2 \pm 2ab + b^2 = (a \pm b)^2$$ - Factoring out the greatest common factor (GCF): $$ax + ay = a(x + y)$$ - Factoring trinomials of the form $$ax^2 + bx + c$$ by finding two numbers that multiply to $$ac$$ and add to $$b$$. 4. Example: Factor $$x^2 - 9$$. 5. Recognize this as a difference of squares: $$x^2 - 3^2$$. 6. Apply the formula: $$x^2 - 9 = (x - 3)(x + 3)$$. 7. Another example: Factor $$2x^2 + 8x$$. 8. Find the GCF, which is $$2x$$. 9. Factor out the GCF: $$2x^2 + 8x = 2x(x + 4)$$. 10. To factor more complex expressions, look for patterns or use methods like grouping or quadratic formula if needed. Factoring helps simplify expressions and solve equations more easily.