1. Let's start by stating the problem: factoring is the process of breaking down an expression into simpler expressions (factors) that, when multiplied together, give the original expression. 2. The most common factoring formulas include: - 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): find the largest factor common to all terms and factor it out. 3. Important rules: - Always look for a GCF first. - Recognize special patterns like difference of squares or perfect square trinomials. - For quadratics, try to find two numbers that multiply to the constant term and add to the middle coefficient. 4. Example: Factor $$x^2 - 9$$. - Recognize this as a difference of squares: $$x^2 - 3^2$$. - Apply the formula: $$(x - 3)(x + 3)$$. 5. Another example: Factor $$2x^2 + 8x$$. - Find the GCF: 2x. - Factor it out: $$2x(x + 4)$$. 6. Factoring helps simplify expressions and solve equations by setting each factor equal to zero. If you have a specific expression you'd like to factor, please share it!