Use the commutative and/or associative laws to rewrite the given expression.  Label each step with a reason.\n\n2+(a+b) as b + (2 + a)
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2 + (a + b)\ngiven\n\n2 + (b + a)\ncommutative prop. of addition\n\n(2 + b) + a\nassociative prop. of addition\n\n(b + 2) + a\ncommutative prop. of addition\n\nb + (2 + a)\nassociative prop. of addition\n\n^_^
327354
well...\n\nAll you have to do is remove one term at a time by multiplying that term by all the other terms in the next set of parenthesis. \n\nStarting at the beginning, with -4b^3:\n\n-4b^3(4x-3)(2b^3-2x^2+b)\n\nmultiplying the first term by each of the terms in the next set of parenthesis gives:\n\n(4x*4b^3-3*4b^3)(2b^3-2x^2+b)\n(-16xb^3 + 12b^3)(2b^3-2x^2+b)\n\nNow, do the same thing with each of the remaining terms, starting with -16xb^3 and then 12b^3:\n(2b^3*(-16xb^3)-2x^2*(-16xb^3)\n+b*(-16xb^3)+2b^3*(12b^3)-                                 2x^2*(12b^3)+b*(12b^3))\n\nAnd that's it. The rest you can work out yourself, I'm sure. I would redo the whole thing on paper yourself, to make sure you understand it, and that I didn't lose any terms, since I just did it on the screen.
510934
(1+1)-2*3/2^2+2\n\nWithout useing Order of Operations: 2\n\nWith Order of Operations: 2.5
213198
((a^2 - b^2)/8a) X ((4a^3)/(a + b)^2))\n(4a^3(a^2 - b^2))/(8a(a + b)^2)\n((4a^3)/(8a)) * ((a^2 - b^2)/(a + b)^2)\n((a^(3 - 1))/2) * (((a - b)(a + b))/((a + b)(a + b)))\n((a^2)/2) * ((a - b)/(a + b))\n\nANS : ((a^2)(a - b))/(2(a + b))\n\nOn your problem, here is where you went wrong\n\nTo make it easier, you should had kept your problem in\n\n(4a^3(a - b))/(8a(a + b)) form, then had done this\n\n((4a^3)/(8a)) * ((a - b)/(a + b))\n\n(4/8)(a^(3 - 1))((a - b)/(a + b))\n(1/2)(a^2)((a - b)/(a + b))\n((a^2)(a - b))/(a + b)
333751
[(2x^3+2x^2+3x+3)/(x^2-9)]*\n[(x^2+2x-15)/(4x^2+6)]\n\nFactor each expression individually.\n\n(2x^3+2x^2+3x+3) = (x+1)(2x^2+3)\n\n(x^2-9) = (x+3)(x-3)\n\n(x^2+2x-15) = (x+5)(x-3)\n\n(4x^2+6) = 2(2x^2+3)\n\nSubstituting these in, our expression becomes\n{[(x+1)(2x^2+3)]/[(x+3)(x-3)]}\n*{[(x+5)(x-3)]/[2(2x^2+3)]}\n\nCombining these into one larger expression, we get\n[(x+1)(2x^2+3)(x+5)(x-3)]/\n[2(x+3)(x-3)(2x^2+3)]\n\nCancel the quantities common to the numerator and denominator and we get our final answer\n[(x+1)(x+5)]/[2(x+3)]\n\nGood luck.
125236
let a = b  \nMultiply both sides by a \na² = ab  \n Add (a² - 2ab) to both sides \na² + a² - 2ab = ab + a² - 2ab  \n Factor the left, and collect like terms on the right \n2(a² - ab) = a² - ab  \n Divide both sides by (a² - ab)\n2 = 1\n(The place where the proof goes wrong is the very last step.  If a² - ab = 0, then you would be dividing by zero, which is undefined.)
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x=A*A\n\nSO\n\nA*A + ? = (A+1)*(A+1) = A*A+2A+1\n\nSO ? = 2A+1\n\n\nand sice you defined X=A*A , A=√(X)\n\nSO ? = 2A + 1 = 2√(X) + 1
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(x+7)(x+3)\n(x-11)(x+2)\nforget this one.  its AC factoring though\nthis ones AC too
456876
S=(c-b)/(b-a)\nSb-Sa-c+b=0\nc=Sb-Sa+b\nc=S(b-a)+b\nHowever you like it.
340282
8x + 7y - (2x - 6y) \nStep 1: 8x + 7y - (2x) -(-6y)\nStep 2: 8x + 7y - 2x + 6y\nStep 3: (8x - 2x) + (7y + 6y)\nStep 4: (6x) + (13y)\nStep 5: 6x + 13y\n1. First, we use the Distributive property. The negative sign in front of the (2x - 6y) implies that it is multiplying everything within the parentheses by -1.\n2. Now we have to fix the signs. Remember: -1 x -1 is positive 1. Thus -(-6y) = 6y.\n3. Now we put the similar terms together.\n4. Now we add and subtract whats inside the parentheses.\n5. Done!\n\nHope I helped. =)
590759
You want to basically simplify the expression through taking out a common factor of each term in that expression:\n\nso 4 goes into both 4a and 16\nso 4(a+4) I believe would be the correct answer. \nDon't get mad if I'm wrong.
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(a + b)^2 = a^2 + 2ab + b^2\n\nso\n\n(a + 1)^2 = a^2 + 2a + 1\n(a - 1)^2 = a^2 - 2a + 1\n\n\n\nFermat:\n\nIf a = 2^(n-1) then\n(a + 1)^2 = (2^(n-1) + 1)^2\n = (2^(n-1))^2 + 2(2^(n-1)) + 1\n =( 2^(n-1)^2 ) + (2^n + 1)\n\n\n\nMersenne:\n\n(2^n - 1) + (2^(n-1) - 1)^2 =\n = 2^n - 1 + (2^(n-1))^2 - 2(2^(n-1)) + 1)\n = 2^n - 1 + (2^(n-1))^2 - 2^n + 1\n = (2^(n-1))^2\n = ( (2^(n-1) - 1) + 1 )^2
70870
y^2 + 3y + 6 -4y^2 - 6y simplifies to:\n\n-3y^2 - 3y + 6\n\nIt's a second-degree trinomial expression.
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(a+b)(b^6-ab^5+a^2b^4-a^3b^3+a^4b^2-a^5b+a^6)\nGood Night, and Good Luck!
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If you have a^2 - b^2\n\nThen the factored form is (a+b)(a-b)\n\nThe third one can be written as: (x+5)^2 - y^2\n\nSo a=x+5\nand b=y\n\n((x+5)+y)((x+5)-y)
564578
[(16x*2-25) / (24x*2-30x)] / [(8x*2-2x-15) / (6x*2-7x-3)]\n= [(16x*2-25) / (24x*2-30x)] [(6x*2-7x-3) / (8x*2-2x-15)\n= [(16x*2-25) (6x*2-7x-30] / [(24x*2-30x) (8x*2-2x-15)]\n= [(4x-5) (4x+5) (3x+1) (2x-3)] / [(6x) (4x-5) (4x+5) (2x-3)]\n= (3x+1) / 6x
500887
Are you missing a plus sign and parentheses around a+b?  If so, then\n(a^2 -2ab + b^2) = (a-b)(a-b) = (a-b)^2\nYou cannot cancel anything, so \n(a^2 -2ab + b^2)/(a+b) does not simplify.\nYou may wish to write it as (a-b)^2 /(a+b)\n\nIf you are not missing a plus sign or parentheses, then\na^2 - 2ab b^2 = a^2 - 2ab^3\nYou can factor out an a.\n= a(a-b^3)  This does not factor, so you cannot simplify.\nDivide this by a and you get a - b^3\nNow add b\nAnswer: a - 2b^3 + b