Factoring Algebraic ExpressionsDate: 6/15/96 at 0:52:47 From: Saul Miller Subject: Factoring algebraic expressions Is this the right place to ask for help on factoring?. If yes, please can you help me with these factoring problems? Factor: 1) (xy+1)(x+1)(y+1)+xy 2) (1-y)^2 x^4-2x^2(1+y^2)+(1+y)^2 3) (b-c)(x-a)^2+(c-a)(x-b)^2+(a-b)(x-c)^2 Date: 6/17/96 at 11:54:8 From: Doctor Paul Subject: Re: Factoring algebraic expressions In number one, you've got a problem like this: [A * B * C] + D Note that [(A*B)*C]+D would yield the same result. Let's begin by multiplying the 'A' and the 'B' terms; that is, (xy+1)*(x+1) When given something in the form (G+H)(I+K), here's how to expand it: G*I + G*K + H*I + H*K When applied to the problem above, we have: (xy*x)+(xy*1)+(1*x)+(1*1) = x^2y + xy + x + 1 So now we've got A*B. We must now multiply that term by 'C' (which is y+1) Now we've got (y+1) * (x^2y + xy + x + 1). Just as when we expanded above, we multiply each term in the first equation (y+1) by each term in the second equation (x^2y+xy+x+1) and then add them up. (y*x^2y)+(y*xy)+(y*x)+(y*1)+(1*x^2y)+(1*xy)+(1*x)+(1*1) Now simplify: (y^2*x^2)+(xy^2)+(xy)+(y)+(x^2y)+(xy)+(x)+(1) Note that we've got two xy's in there so let's add them up: x^2y^2 + xy^2 + x^2y + 2xy + x + y + 1 Problems 2 and 3 use the same rules mentioned above. Why don't you try them yourself? If you still have trouble, write back and we'll help you again. -Doctor Paul, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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