Adding and Subtracting PolynomialsDate: 12/08/96 at 13:57:10 From: Anonymous Subject: Adding and subtracting polynomials Dear Dr. Math, Could you pleeeease explain to me how to add and subtract polynomials? I'm having so much trouble with them! Thanks, James Todd Date: 12/10/96 at 16:18:07 From: Doctor Lisa Subject: Re: Adding and subtracting polynomials Hi James! I'm just getting ready to teach this to my students tomorrow, so you're in luck! I happen to have some examples right here. Add the following: (4x - 2x^2 - 7xy) + (2x^2 + 5xy) When you are adding (or subtracting polynomials), you must find the variables and exponents that match. For example, in the problem above, -2x^2 and 2x^2 have the same variable and exponent. So do -7xy and 5xy. Both the variables and the exponents each variable has must match exactly or you can't add (or subtract) them. It's just like if you tried to add x and y -- you couldn't do it because they are different. Once you find that something matches (like -2x^2 and 2x^2), then you add the coefficients (remember, that's the number in front). So this is what happens: 4x: there is nothing to add with it, so we leave it alone, but include it in the answer -2x^2 + 2x^2 = 0x^2, so we won't have an x^2 term in the answer -7xy + 5xy = -2xy So the answer is 4x - 2xy. Here's another with addition: (4 - 5x^2 + 7x^3) + (4x^3 + 5x^2 + 5x^4) We usually start with the highest power of the variable and work our way down. Here goes: 5x^4: nothing to add to it, so we leave it be 7x^3 + 4x^3 = 11x^3 -5x^2 + 5x^2 = 0x^2 (so there will be no x^2 term in our answer) 4: nothing to add to it, so we leave it alone The answer is 5x^4 + 11x^3 + 4. Subtraction is very similar to addition. You can think of it in one of two ways. You can think of it as subtracting the coefficients (instead of adding them) OR you can think of it as adding the negative of the coefficients. Here are a couple of subtraction problems: (8x^3 + x^2 - 7x - 11) - (5x^3 + 3x^2 - 3x + 8) When I teach this to my students, I tell them to go through and distribute the negative sign to the second group. I tell them to do this because sometimes when you go to subtract, there isn't a like term in the first group. However, you still need to make the sign in front of the number you're trying to subtract the opposite of what you are given. By distributing the negative, you make sure to properly take care of these terms. So I would do this first: (8x^3 + x^2 - 7x - 11) - 5x^3 - 3x^2 + 3x - 8 Now we have a situation like the one we had before with addition: 8x^3 - 5x^3 = 3x^3 x^2 - 3x^2 = -2x^2 -7x + 3x = -4x -11 - 8 = -19 So the answer is: 3x^3 - 2x^2 - 4x - 19 Here's another: (4a^2 - 6a) - (2a^2 + 5a - 3) Taking care of the negative I get: (4a^2 - 6a) - 2a^2 - 5a + 3 Combining like terms: 4a^2 - 2a^2 = 2a^2 -6a - 5a = -11a 3: this stays as 3 since there is nothing to add to in the first set So the answer is: 2a^2 - 11a + 3 I hope this helps you out! -Doctor Lisa, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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