Factor out 16x4-1? the 4 is the exponent of your confused?
912614
To expand on what Emily said, you can take the difference of two squares again.\n\n(16x^4 - 1)\n(4x^2 - 1) (4x^2 + 1)\n(2x - 1) (2x + 1) (4x^2 + 1)
216863
((4 * 4) / 4) - 4 + 4 = 4
734250
4 sqrt 16x + 5 sqrt 16x = 9 sqrt 16x\n\n= 9 sqrt 16 sqrt x\n= 9 * 4 sqrt x\n= 36 sqrt x
297354
For all those people giving the answer\n4/4+4*4 = 20\nyou need to learn the order of operations!!\nIn this problem the first operation performed is multiplication or division in the order in which they appear.\nFor the problem division is done first.\n4/4 = 1\nThus the problem becomes\n1+4*4  Now there is still multiplication in the probem so that has to be done before the addition.\nHence, 4*4 = 16\nThus, the problem is now\n1 + 16\n= 17 and does not equal 20.\nIf there were parentheses (other people have already done this), then you could say\n(4/4+4)*4 = 20 because then you could add the 4 and the 1 together first because operations inside parentheses are performed before the other operations.\nSo you have\n(4/4+4)*4\n= (1+4)*4\n= 5*4\n= 20\nHowever, I'm not sure parentheses are allowed to be included because now there are 5 symbols being used instead of 3.\nI would use the symbols !, / and -\nThe exclamation point means factorial.\n4!4/4-4   First evaluate 4! (4! = 4*3*2*1 = 24) and then multiply by 4\n96/4-4   Now 96/4 = 24\n=24-4\n=20
598932
Replace y in the first expression by the value from the second.  You get:\n8x - 4(2x - 4) = 16\n\nNow simplify:\n8x - 4*2x - 4*-4 = 16\nthat's four times minus four...\n8x - 8x - -16 =16\n16 = 16\nThis holds for any value of x.\nThis has occurred because the two expressions are the same!\nIf you divide the first expression by 4, you get:\n2x - y = 4\nnow make y the subject (add y to both sides, then take 4..)\n2x - 4 = y\n\nIf you were to substitute your solution into the second expression, you would have:\n-1 = 2*3 - 4   clearly this is not a solution...\n\nIf x were 3 then y would be 2*3-4 = 2\n\nI hope the explanation above is of some use!
1187773
Complete the square is referring to having a problem like \ny=16x^2 + 64x + 5\nor something similiar where factoring is not possible.\nYou can then take the equation & change it like so\ny=16(x^2 + 4x + ____) + 5 \nNotice that this equation is still the same as before, but it has been re-arranged. Now, notice that if you add 4 you can then reduce what is inside of perentheses to (x+2)^2\ny=16(x^2 + 4x + 4 - 4) + 5 \n\nNotice that since you added 4 and subtracted 4, you have done nothing\n\nNow, you can factor the (x^2 + 4x + 4)=(x+2)^2\n\ny=16((x+2)^2 - 4) + 5\n\nDistribute 16 \n\ny=16(x+2)^2 + 5 - 64\n\ny=16(x+2)^2 - 59 \n\nThis represents the same equation that you had at the beginning but can be a much easier form to work with.\n\nWe started with\ny=16x^2 + 64x + 5 \n      x=2,y=197   & (0,5)\nand wound up with\ny=16(x+2)^2 - 59 \n      x=2,y=197   & (0,5)\nPoints just to show they are equal equations.\n\n\nThis is very useful in math. You may not find it too useful unless you are a little farther along, but in situations involving circles, or integration techniques this can come in very very handy.
811480
1)  I'm afraid I don't understand the question.  It's possible that  you've been taught a different technique than I teach.  The method I teach is essentially the long division you learned in third/fourth grade, modified to work with polynomials.  I'm afraid I'm no help there.\n\n2)  Those are patterns.  You need to understand them and learn to recognize them.  For instance:\n\nx^2 - y^2\n\nis a difference of squares.  That means it will factor into (x+y)(x-y).\n\n9a^2b^4 - 4x^6\n\nis also a difference of squares.  It will factor into\n\n(3ab^2 - 2x^3)(3ab^2 + 2x^3)\n\nThat's what I mean by being able to recognize them.\n\n3)  The only other thing that's important is that the pattern repeats forever.  i^5 = i, i^6 = -1, and so on.  So, i^400 = 1.\n\nAs for the rest of question 3 - well, it depends on what you're being asked.  If you're asked to find all of the rational solutions, then of course you'd find the rational solutions.  If you're asked to find ALL of the solutions, that would certainly include the rational ones.  If you're asked to find all imaginary or complex solutions, then you wouldn't necessarily look for the rational ones, but it might make it easier to solve the problem if you did.  As a thumbrule, I'd suggest always looking for rational solutions unless you have a specific reason not to.\n\nAs for your additional question:  x^2 + 16 = (x+4)^2 just doesn't work.  Try reversing it:\n\n(x + 4)^2 = (x + 4)(x + 4) = x^2 + 4x + 4x + 16 = x^2 + 8x + 16\n\nYou're missing the cross-terms if you try to factor x^2 + 16 that way.  In fact, a sum of squares does not factor over the real numbers.\n\nIf you're ever unsure why a particular factoring pattern doesn't work, you will almost always get an answer by trying it the other way.
200291
The factor common to the first 2 terms in #1 is 3x^4 because both terms are divisible by that (take the GCF of the numbers in front, and the lower of the two exponents).\n\nFor the second pair, the common factor is 4\n\nSo you'd get 3x^4(3x + 2) - 4(3x - 2) if you have to actually factor them\n\nProblem 2, the common factor of the first 2 terms is 4x^3 and for the second pair, 1.\n\nSo you'd get 4x^3(5x + 4) - 1(5x + 4)  which becomes\n\n(4x^3 - 1)(5x + 4).
117122
If you mean 16x^2=49 then here is the answer. Subtract 49 from both sides. 16x^2-49=0. This is the difference between squares so it factors to (4x+7)(4x-7)=0. Set each factor equal to 0. \n            4x+7=0\n            4x-7=0\n Then solve. The answers are x=-7/4 and x=7/4
777394
factor out 4b\n\n4b(b-2)= 0\n\nb = 2, 0\n\ngoodluck ^_^
323323
This is the best I could come up with:\n\n(a)  (x^2-4)(x^4+4x^2+16)\n      (x-2)(x+2)(x^4+4x^2+16)\n\n(b)  (x^3-8)(x^3+8)\n     (x-2)(x^2+2x+4)(x+2)(x^2-2x+4)\n\n(c)  If you take out the factors that are the same, what's left should be equal hence:\n     x^4+4x^2+16=\n(x^2+2x+4)(x^2-2x+4)\n\n(d)  x^(a^2)+2ax^a+4a^2=\n(x^a+ax+2a)(x^a-ax+2a)
866262
a. 12           16/4=4   4x3=12      or     3/4= 0.75   0.75x16=12\n\nb. first u need to find a common denominator so put it all in fractions  3 x ? = 12        we need to change the 1 to a 5 so we\n                5    ?     1         multiply by 5, since we multiplied the\n                                        1 then we need to multiply the 12 by the \n                3 x ? = 60         same to get 60 so now we have...\n                5    ?     5\n                                             so now we just have to fill in the ? by multiplying 3x20=60    and 5x1=5    so 20over one is simply 20\nso (3/5x20=12)\n\nc. well this depends if the numbers have to be same, if not then just put in any number for the first since ( ), multiplication and division are always done first and then fill in the rest to match\n\nso lets get the first one down to a lower number so it will be easier  25(8 x -1 + 10)  8 x -1 = -8   (-8+ 10) = 2\n(25 x 2 = 50)      since the answer is 3 the 50-3=47 so now we have to figure out what number to put in to get 47\nso lets reverse the equation 47 / 2 = 23.5 and so we add 1  24.5\n\n2(24.5-1)=47      50-47=3\n\nso the final equation is 25(8 x -1 + 10) - 2(24.5 -1) = 3
504201
Actually, none of the above are correct. To factor anything in the form of a cubed - b cubed, where a and b are real numbers, the formula is (a - b)(a^2 + ab + b^2). In this case, the a would be 1 and the b would be 4. So, the answer would be (x-4)(x^2 + 4x + 16i)\n\nand paul is incorrect also, try to multiple it out, it's wrong
387267
Factor a^2 + 8a + 16\na^2 + 8a + 16 = \n(a+4)(a+4) =\n(a+4)^2\nNow \n(a^2)+8a+16-(b^2)\n= (a+4)^2 - b^2\nThis is a difference of squares.\n(a+4+b)(a+4-b)
152774
I'm not sure if the x is supposed to be the multiplication symbol or a variable.\n\nIf you mean 2*(4*2) or 2(4*2), the result is: 16\n\nIf it is the letter "x", the answer is:\n2x(4*2) = 2x(8) = 16x
883726
when multiplying, exponents with like bases add, therefore\nn+1+n-1 =2n and your answer is x^2n
554663
An example:\n1234/16 = 77.125\n1234/16/16 = 4.8... smaller than 16. Stop this.\n\n16x16=256\n1234 = 4 x 256 + 210\n210 = 13 x 16 + 2\n1234 = 4 x 256 + 13 x 16 + 2 That is it or hex: 4D2