Final answer:
To unfoil quickly, use the reverse foil method. Identify the first and last terms of each binomial, multiply them, and rewrite the middle term as the sum of the products. Example: (x + 2)(x - 3) = x^2 + 2x - 3x - 6.
Step-by-step explanation:
To unfoil quickly, you can use a shortcut called the reverse foil method. Reverse foil allows you to quickly determine the original factors of a quadratic expression that has been expanded using the distributive property. Let's say we have the expression (x + 2)(x - 3) and we want to unfoil it. Start by identifying the first term of each binomial, which in this case is x from (x + 2) and x from (x - 3). Multiply these two terms together to get x^2. Then, identify the last term of each binomial, which is 2 from (x + 2) and -3 from (x - 3). Multiply these two terms together to get -6. Finally, rewrite the middle term of the expanded expression as the sum of the two products obtained: (x^2 + 2x - 3x - 6). In this way, you can unfoil the expression quickly and identify the original factors without having to expand it fully.