Distributive LawDate: 8/2/96 at 17:50:40 From: Anonymous Subject: Distribution of Subtraction I am an English teacher trying to teach Algebra to high school students and I need a lot of help. Regarding the following equation: [(2y)(squared) + 8] - (y (squared) - y) = 3y sq The 1st step of the solution in my text is: (4y sq + 8) - y sq + y = 3y sq My question: Why does "-(y sq - y)" become "-y sq + y?" Why does the subtraction symbol change to addition? Thank you. Date: 8/5/96 at 0:6:44 From: Doctor Mike Subject: Re: Distribution of Subtraction Hello, You are NOT the first person in history to get hung up on this point. This is a form of (or really a consequence of) the Distributive Law. The most common version of the Distributive Law is: A*(B + C) = A*B + A*C It says that to multiply a sum of 2 numbers by A, you multiply each one of them individually by A, and then add those 2 results together. Another common version of the Distributive Law is: A*(B - C) = A*B - A*C This looks different from the first one above, but it really isn't a new and different property of numbers. Here's why it follows : Since "B - C" (B minus C) is the same as B + -C (B plus the negative of C), it is true that "A*(B - C)" is the same as "A*(B + -C)". So using the first version of the Distributive Law from above, A*(B - C) = A*(B + -C) = A*B + A*(-C) = A*B - A*C Now, finally, what you have been waiting for. An expression such as -(B - C) is the same as (-1)*(B - C), so -(B - C) = (-1)*(B - C) = (-1)*B - (-1)*C = -B -(-C) = -B + C By the way, the reason for that last step was that the "negative of the negative of C" is just C. See? In your particular example "-(y sq - y)", B is y squared and C is y. I hope this gets you and your class started in the right direction. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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