Multiplication of Polynomials
Date: 3/20/96 at 16:2:26 From: Anonymous Subject: multiplication of polynomials I need to find the product for these two problems: 1. 7(4m-3)(2m+1) 2. (2x-1)(3x exp.5 -2x exp.3+x exp.2-2x+3)
Date: 3/21/96 at 22:26:30 From: Doctor Steven Subject: Re: multiplication of polynomials For these two problems you need to use an algorithm called FOIL. FOIL stands for first*first outer*outer inner*inner and last*last. So we'll do the first problem first (imagine that) 1. Find 7(4m - 3)(2m + 1). Step 1) Multiply 7 and 4m - 3 to get: 28m - 21. Now the problem looks like (28m - 21)(2m + 1). Step 2) Use FOIL. first * first = 28m * 2m = 56m^2 (56m exp.2 in your writing) outer * outer = 28m * 1 = 28m inner * inner = -21 * 2m = -42m last * last = -21 * 1 = -21. Step 3) Add the results from step 2 up to get: 56m^2 + 28m - 42m - 21. Step 4) Simplify to get: 56m^2 - 14m - 7 That's your answer. 2. Find (2x - 1)(3x^5 - 2x^3 + x^2 - 2x + 3) This one's a little harder since you can't use FOIL on it (FOIL only works on multiplications of things with two terms), but it is still do-able so don't lose hope. Step 1) Multiply everything in second polynomial by 2x to get: 6x^6 - 4x^4 + 2x^3 - 4x^2 + 6x. Step 2) Multiply everything in second polynomial by -1 to get: -3x^5 + 2x^3 - x^2 + 2x - 3. Step 3) Add these results together to get: 6x^6 - 3x^5 - 4x^4 + 4x^3 - 5x^2 + 8x - 3. That's your answer. Hope this helps, on this problem and on future ones. -Doctor Steven, The Math Forum
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