Use the commutative and/or associative laws to rewrite the given expression. Label each step with a reason.?
459181
Is the symbol "&" just a part of the problem?\n(&2)m\nCommutative law of multiplication says you can switch the order in which things are multiplied.\n&2 = 2&\nThus,\n(&2)m = (2&)m\nThe associative law of multiplication says you can move the parentheses.\n(2&)m = 2(&m)
576001
By the transitive property, a=c
658708
this one isn't possible..wait...i think i got it....\n\nxa+yb+xz+yz\nxa+yb+z(x+y)\n\nif a typo, and a = b then:\nxa+ya+z(x+y)\na(x+y)+z(x+y)\n(a+z)(x+y)\n\notherwise, not possible unless, use the math trick:\nxa+yb+z(x+y)+ya-ya+xb-xb\nxa+xb+ya+yb+z(x+y)-xb-ya\n(x+y)(a+b)+z(x+y)-xb-ya\n(x+y)(a+b+z)-xb-ya
771836
Simple substitution.\n\n5(3) - 2(2) + 4(4)\n15 - 4 + 16\n27
372419
I fear you have a missing element here... do you want the differencial of 4P^2..etc because if so you need to know what 4P^2..etc equals, or is 4P^2..etc the differencial of another expression, because if so your question is a bit like saying what is the answer to x=2\n\nIf you want to differencial of 4P^2..etc then I suggest you solve the original equation for t which will make the algebra easier and then use the chain rule where dP/dt = [1/(dt/dP)]
836231
8r@+2rs@+7r@s [ I think you have typed = in place of + by mistake]   .When you want to simplify an algebric expression ,you should put together all terms having the same algebric variables for example if you want to simplify 2a-3b+6a+5b,you should first write this as 2a+6a-3b+5b and now add2a and 6a giving you 8a and -3b and +5b giving you +2b,The answer would be 8a +2b.please remember only similar algebric varibles can be added or subtracted .So when you add 12x with 5y ,as you cannot add them conventionally,your answer would be 12x+5y.Another method is that the algebric variable are not totally similar but part of them are simila.In that case it is best to take the part similar variable as common from each term while simplifyiung.in the problem you have given though none of the variables ar similar each of them contains "r" so we shall simplify it in this way  r(8r+2s@+7rs) and that is the answer.If i have failed to make you understand anything,you may send an e-mail to me at sarkartpas2005@yahoo.com and I shall be too happy to explain the process again
763185
I believe he wants you to write the given equation in the standard form for YSUB1 whatever that is.\n\nGuido
67585
Formulaically it reduces down to x*z = x*z, so no matter which numbers you plug in for any of the values it will be a valid equation.  \n\n(x*(y+z))-(x*y)=x*z      becomes\nx*y + x*z - x*y = x*z     rewrite that as \nx*y + x*z + -(x*y) = x*z    the positive and negative x*y terms cancel,leaving\n\nx*z = x*z\n\nSince that is a truism, an infinite number of solutions exist.
364344
emmmmmm\n\nd. its not a fuction of x in terms of y explicitly. It needs to be rearranged
846821
the way you communicate to one another using algebraic symbols?
782057
look at a few examples and it will make sense\n\nfor example \n\n02 (where the 2 is small)   -> _ O    (the _ is where a number goes)  (2)
650155
simple\nfirst\nwhen we apply ∑ we can write the series as\n(a_2 - a_1) + (a_3 - a_2) + (a_4 - a_3).... (a_n - a_n-1) (a_n+1 - a_n)\n\nwhen u add \nthe terms starting frm a_2(except a_1 & a_n+1) get cancelled with the correseponding terms and u get\na_n+1 + a_1
634747
What you want is express \n\nv = a*v1 + b*v2 + c*v3 \n\nWhere a, b and c are, of course, scalars. The coordinate vector will then be (a, b, c).\n\nNow how do we do this: \n\n(2, -1, 3) = a(1, 0, 0) + b(2, 2, 0) + c(3, 3, 3) \n\nEither you just look at it and try to guess what a b and c can be, or you write this up as a set of 3 equations in a,b and c: \n\n2 = 1a + 2b + 3c\n-1 = 0a + 2b + 3c\n3 = -0a + 0b + 3c \n\n...and then solve it: \n\nFrom the last equation we see that c = 1, then using the second equation, -1 = 2b + 3  <=>    -4 = 2b  <=>  -2 = b\n\nAnd substituting into the first, \n\n2 = 1a + 2(-2) + 3(1) = a - 4 + 3 = a - 1 \n\nthus 3 = a. \n\nSo the coordinate vector is (3, -2, 1) and with these numbers the criteria are (supposedly) satisfied. :)
940318
General principle:  if you have an equation (something with an equals sign in it), you can do anything you want as long as it's mathematically valid and you do it to both sides.  Do that, and you'll still have an equation.\n\n4y - 2x = 8\n\n4y - 2x + 2x = 8 + 2x\n\n4y = 8 + 2x because the -2x and +2x add to 0.\n\n4y = 2x + 8 because addition is commutative.  It doesn't matter what order you add them in.\n\nAt this point, we have 4y on one side of the equation and we're trying to get y by itself.  Obviously, we need to get rid of the 4.  We're currently multiplying by the 4, so we get rid of it by dividing by 4.\n\n4y/4 = (2x + 8)/4\n\ny = 2x/4 + 8/4 by the Distributive Property\n\ny = (1/2)x + 2\n\nSo, to write it as a function,\n\nf(x) = (1/2)x + 2
222592
1. p'q\n\n2. p'\n\n3. pq' + p'\n\nI think i got the correct ones !
1068964
simplify expression: -2(y+3)+6(y+1)\n\nsimply distribute then add.
794749
This shall work.\nhttp://pubs.logicalexpressions.com/pub0009/LPMArticle.asp?ID=305