find mistake and win 10points\na=b\na*a=ab(multiplying by a on both sides)\na*a-b*b=ab-b*b(subtracting by b*b)\n(a+b)(a-b)=b(a-b)\na+b=b\nb+b=b\n2b=b\nthrefore2=1\nif correct mistake found then surely 10points.\ntherefore 2=1
138141
The first answer came from -J. is completely right and since he/she was the first one who answered the question correctly I think he/she deserves the 10 points.
103890
This is how I remember it...hope it helps.\n\nA Proof\nLet a and b be any two real numbers. Consider the number x defined by\n\nx = ab + (-a)(b) + (-a)(-b).\n\nWe can write\nx = ab + (-a)[ (b) + (-b) ]       (factor out -a)\n  = ab + (-a)(0)\n  = ab + 0\n  = ab.\n\nAlso,\nx = [ a + (-a) ]b + (-a)(-b)      (factor out b)\n  = 0 * b + (-a)(-b)\n  = 0 + (-a)(-b)\n  = (-a)(-b).\n\nSo we have\n      x = ab\nand\n      x = (-a)(-b)\n\nHence, by the transitivity of equality, we have\n\n      ab = (-a)(-b).
33882
How about this? Straight multiplying gives you the following:\n\n18b^3/b^2\n\nb^3 = bxbxb\nb^2 = bxb\n\nYou have 3 bs on top and 2 on bottom. Whenever you have the same number on top and bottom, it cancels out. Since there are 2 bs on bottom, 2 of the ones on the top cancel out as well. This leaves you with 18b.\n\nDid that help at all?
427595
a^2 - 2ab + b^2 = (a - b) ^2\n\nthen...\n\n(a - b)^2 / (a + b) = (a -b) (a - b) / (a + b)
170230
1 = b\n2 = d\n3 = d\n4 = c\n5 = c\n\n4/5
55355
(a+b)(a-b) \n= a^2 - ab + ba - b^2\n= a^2 - b^2 -ab +ab\n= a^2 - b^2
205228
ten points if you can figure this out first .. right?? \n\n\nANU!!
311878
1. A & B cross  -  2\n2. A returns    -  1\n3. C & D cross  -  10\n4. B returns    -  2\n5. A & B cross  -  2\n\nTotal minutes: 17\n:)
491301
Let your 2-digit number be represented by 10A + B.\n\nThen, we are given :\n(1) A + B = 6\nand\n(2) AB = (10A + B) / 3\n\nFrom (1) we get B = 6 - A\n\nSubstituting this into (2) gives :\nA(6 - A) = (10A + 6 - A) / 3\n\n6A - A^2 = (9A + 6) / 3 = 3A + 2\n\nTherefore, A^2 - 3A + 2 = 0\nFactorise to give : (A - 1)(A - 2) = 0\n\nThus A = 1 or 2.\n\nIf A = 1, then B = 5.\nIf A = 2, then B = 4\n\nThere are thus 2 solutions for AB.\nAB = 15 or 24.\n\n(It helped to see the question in words)
244459
Say a and b\na-b = 10 and a*b = 999\na = b+10 substituting this in another equation\n(b+10)*b = 999\nb^2+10b = 999\nb^2 + 10b - 999 = 0\nb^2 + 37b - 27b - 999 = 0\nb(b+37)-27(b+37) = 0\n(b+37)(b-27) = 0\nSo,\nb = -37 or b = 27\nand as a = b + 10\na = -27 or a = 37
256392
please dont hate math\nshow interest\nthen you do well\n\nFOIL\nFirst-Out-Inner-Last\n\nThis method is used for multiplying two binomials.\nsay (a+b)(x+y)\n\n( a + b ) (x + y)\n\nFirst------first terms in the two binomials. they are to be multiplied. so ax\nthen Outer a and y. so ay\nInner-----bx\nLast-----last terms in the binomials. so 'by'\nthen add all the terms.\nax+ay+bx+by\n\nyou may consult me
673383
ABC+ABD+C'D\n=ABC+ABD(C+C')+C'D\n=ABC+ABCD+ABC'D+C'D\n=ABC(1+D)+C'D(AB+1)\n=1ABC+1C'D\n=ABC+C'D
545722
I've seen one variant that goes like this:\nLet a and b be equal non-zero quantities\n\n          a = b\n\nMultiply through by a\n\n          a2 = ab\n\nSubtract b2\n\n          a2 − b2 = ab − b2\n\nFactorize both sides\n\n          (a − b)(a + b) = b(a − b)\n\nDivide out (a − b)\n\n          a + b = b\n\nObserving that a = b\n\n          b + b = b\n\nCombine like terms on the left\n\n          2b = b\n\nDivide by the non-zero b\n\n          2 = 1\n\nQ.E.D.\n\nThe problem here is that dividing by (a-b) is dividing by zero, which is an undefined operation.
416988
(1) First one is copied wrongly by you                                            (2) Where is the equal to sign?                                                        (3)This equn. also cannot be solved                                              (4)-p/16+5=9  Multiplying all the terms by 16 ,we get -p+80=144   =>-p=144-80=66 Therefore p=66 YOU SHOULD BE MORE CAREFUL BEFORE SENDING YOUR PROBLEMS TO YAHOO ANSWERS.HOWEVER,YOU MAY SEND THE CORRECTED VERSION OF THE PROBLEMS TO ME IMMEDIATELY THROUGH YAHOO ANSWERS.
477741
My old math teacher showed me this.\n\nSince A=B, then A-B=0, and you can't divide by 0
477333
Hi, \n\nI'll help with the first one, the rest are similar so this should help:\n\n8(k+3)=12k-4\n\n8*k +8*3 = 12k - 4\n\n8k + 24 = 12k - 4\n\n8k + 28 = 12k \n\n28 = 4k\n\nk = 28/4 =7\n\nGood Luck!\nMatt\n\nP.S. I think it's ironic that someone who misspells 2/3 of the words in her post is calling someone else retarded. Seriously, is her time that valuable that she needs to abbreviate the word 'your'?
240546
Well... Well... Well... Mine is the best answer, I guess...!!! It's actually the division by zero, since      a-b=zero! 10 points 4 me!!!