1. The problem is to understand what you need to know about factoring algebraic expressions. 2. Factoring is rewriting expressions as products of simpler expressions. 3. Important formulas and rules include: - Difference of squares: $ (a+b)(a-b) = a^2 - b^2 $ - Perfect square trinomials: $ (a+b)^2 = a^2 + 2ab + b^2 $ - Common factor extraction: $ ax + ay = a(x+y) $ 4. You should recognize patterns like: - $x^2 - 1 = (x-1)(x+1)$ (difference of squares) - $x^2 + 18xy + 81y^2 = (x+9y)^2$ (perfect square trinomial) 5. Practice factoring by: - Extracting common factors - Using special products formulas - Factoring trinomials into binomials 6. Check your factorizations by expanding back to the original expression. 7. Understanding these basics will help you solve the problems shown and similar ones. Final answer: You need to know how to identify and apply factoring techniques including common factors, difference of squares, and perfect square trinomials.