Problem: Write an article based on this summary: Examine the problem. Use FOIL to distribute the terms appropriately. Multiply the constants. Multiply the variables. Combine any like terms and write your final answer.

Answer: A problem involving a two binomials will involve two polynomials, each with two terms that are separated by either a plus sign or a minus sign. A polynomial problem involving two binomials will look something like: (ax + by) * (cx + dy) Example: (2x + 3y)(4x + 5y) FOIL is an acronym used to explain how terms are distributed. Distribute first terms, outside terms, inside terms, and last terms. After this, your rewritten polynomial problem will effectively look like: (ax)(cx) + (ax)(dy) + (by)(cx) + (by)(dy) Example: (2x + 3y)(4x + 5y) = (2x)(4x) + (2x)(5y) + (3y)(4x) + (3y)(5y) The constants refer to the numerical digits in the problem. These are multiplied as they usually would be according to the standard times table. In other words, during this part of the problem, you are multiplying a, b, c, and d together. Example: (2x)(4x) + (2x)(5y) + (3y)(4x) + (3y)(5y) = 8(x)(x) + 10(x)(y) + 12(y)(x) + 15(y)(y) The variables refer to the letters in the equation. When you multiply these variables, different variables will simply be combined together. When you multiply a variable by a like variable, though, you raise that variable by another power. In other words, you are multiplying the the x and y portions of the equation. Example: 8(x)(x) + 10(x)(y) + 12(y)(x) + 15(y)(y) = 8x^2 + 10xy + 12xy + 15y^2 This type of problem is complex enough to potentially produce like terms, meaning two or more end terms that share the same ending variable. If this happens, you should add or subtract the like terms as needed to determine your final answer. The result will look something like: acx^2 + adxy + bcxy + bdy^2 = acx^2 + abcdxy + bdy^2 Example: 8x^2 + 22xy + 15y^2

Problem: Write an article based on this summary: Recognize that your cat phobia is likely being exacerbated by unhelpful thoughts. Make a list of all the negative and unhelpful thoughts that you experience when you are near cats. Replace the negative thoughts with more helpful thoughts.

Answer:
Most people who are afraid of cats are already aware that cats are pretty harmless. However, they have a fear response that is initiated in the brain that they can't currently control. Phobias are often learned behavior. A person may have one bad experience with a cat, he may have subconsciously begun to associate cats with negative things such as illness, or he may have "learned" to be afraid of cats by watching his parents' fearful behavior around them when he was a child. Multiple brain regions are involved in phobias. Therefore, it will take you some time to retrain your brain to think and respond differently to cats. When you are able to identify those unhelpful thoughts, then you can begin to evaluate them. You will probably see that most of these thoughts fall into one (or more) of these three cognitive distortions: Fortune telling is when a person assumes they know what the outcome of a situation is going to be without any true evidence to support it. For example, you may think "This cat is going to scratch me" even though you've never had any interaction with that cat before. Overgeneralizing is when a person takes one specific event and generalizes it to all events. For example, you may think "My friend's cat scratched me two years ago therefore all cats are vicious." Catastrophizing is when you predict that a negative outcome is going to occur and believe that when it does, it will result in a catastrophe. Catastrophizing is when you assume a situation is going to be the absolute worst case scenario. For example, you may think "If the cat scratches me, I will get an infection and die." You can do this by creating alternative statements to counteract the negative thought. When doing this, you are essentially retraining your subconscious to release the unhelpful cognitive distortions and replace them with more positive beliefs. Focus on replacing the negative thought with a positive statement that helps you emphasize neutral or more positive outcomes. For example, you could replace the thought "This cat is going to scratch me" with a statement like "Many people interact with cats every day and do not get scratched." You can even begin by using statements that are less negative then your original thought. For example, you could replace the thought "If the cat scratches me, I will get an infection and die" with the less negative statement, "The worst thing that could happen is that the cat scratches me and runs away. I've been scratched before and it's not so bad. I won't likely get an infection." Eventually you can replace the less negative thought with something even more positive. Try to do this whenever a negative thought pops up. Eventually you'll begin to think more positively about cats.