Negative Coefficients, Subtraction -- and Combining Like Terms?Date: 09/21/2009 at 23:48:28 From: Anuj Subject: How do you combine like terms The directions say to combine like terms and simplify: -9x - y + 1 + 5y + 5x - 10. My answer was 4x - 4y - 9. But I'm not sure if I'm supposed to add or subtract when the numeral/variable is negative/positive. Am I adding and subtracting them right? Date: 09/22/2009 at 11:27:13 From: Doctor Ian Subject: Re: How do you combine like terms Hi Anuj, The basic idea behind combining terms is that you're applying the distributive property. With constants, this might look like 3*5 + 8*5 = (3 + 8)*5 = 11*5 Does that look familiar? Well, you can do the same thing with variable terms, e.g., 3x + 5x = 3*x + 5*x = (3 + 5)*x = 8*x = 8x The only thing that changes really is that some of the multiplication symbols are left implied, rather than written out. Suppose I have something like 3x + 4y + 5x + 6y Addition is commutative, so I can change the order to get "like" terms together, 3x + 5x + 4y + 6y and then I can combine them, (3 + 5)x + (4 + 6)y = 8x + 10y So far, so good? Okay, what if I have subtractions -- like you had in your expression? 3x - 4y - 5x + 6y Now, subtraction is NOT commutative; but every subtraction can be written as an addition: 3x + -4y + -5x + 6y And this puts me back in the same boat as before: 3x + -4y + -5x + 6y = 3x + -5x + -4y + 6y = (3 + -5)x + (-4 + 6)y = -2x + 2y One last wrinkle: sometimes you don't see a coefficient, e.g., x + 4x + 7x If it helps, take that implied coefficient of 1, and make it visible: x + 4x + 7x = 1x + 4x + 7x = (1 + 4 + 7)x = 12x (Are you seeing a pattern here? An awful lot of math is just looking at what's in front of you, and asking yourself if there's some way to rewrite it so that it will be easier to work with!) Does that make sense? Try your expression again, and let me know what you come up with, okay? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 09/22/2009 at 22:39:31 From: Anuj Subject: Thank you (How do you combine like terms) Thank you very much. I got a A+++ on my test because of your help. Thank you so much! |
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