(4x + 1)(4x - 1)
You can think of this like any other factoring problem.
16x2 - 1 is just like 16x2-0x -1, which shows you that the two terms that just have x in them cancel each other out. That means that they have the same coefficient, and opposite signs.
So looking at 16, it can be split into 4 and 4. These are the front coefficients of each section. Then, you know that to get a negative one, you have to have a positive one in one chunk, and a negative one in the other. Then, when you foil it out, the term with a single x is gone, and you prove that the answer is right.
2(x^2 - 8)
It can't be factored because its discriminant is less than zero.
(x - 16)(x + 2) x = 16 or -2
The answer is 4 squared minus 2 squared as 4 squared is 16 minus 2 squared, which is 4, gives you 12 as an answer.
Pull out the common factor of 2 ... 2(y^2+6y-16) Then just factor (y^2+6y-16) ... (y-2)(y+8)
It is: 5(x^2 -16)
2(x^2 - 8)
75r^2-48 You can take out 3.So... 3(25r^2-16) 3-parenthesis-25r squared-minus-16-parenthesis (:
It is the difference of squares. (x-4) and (x+4) <--- answer
The square root of 25a squared is 5a. The square root of 16 is 4.So the answer is (5a+4)(5a-4)
14x2-7x2-16 7x2-16 (this can't be simplified any more)
It can't be factored because its discriminant is less than zero.
(x - 16)(x + 2) x = 16 or -2
The answer is 4 squared minus 2 squared as 4 squared is 16 minus 2 squared, which is 4, gives you 12 as an answer.
In one bracket, write 16 times the square root of 2 minus 3x. In the other one, write 16 times the square root of 2 plus 3x.
62 - 16 = 20
Pull out the common factor of 2 ... 2(y^2+6y-16) Then just factor (y^2+6y-16) ... (y-2)(y+8)