I need help factoring?

Question

These are the four problems I cant do.

4X^2-1

4X^2-2X

X^2-4X+4

2X^2-3X-2

Answer 1

sorry

Answer 2

Whenever you see something of the form a^2-b^2, the answer is a^2 - b^2 = (a-b)(a+b). In your first problem, a= 2x because a^2=4x^2 and b = 1 because 1^2 = 1. Therefore :
4x^2-1 = (2x-1)(2x+1)

In the second problem look for what's common to 4x^2 and 2x.
The answer is both terms contain 2x, so you can factor it out as follows; 4x^2-2x=2x(2x-1)

The next problem you should set up (x-?)(x-?). You know the first term in each factor must be x because that's the only way you can get x^2. The last term has to be 2 because 2*2=4 or one term must be one and the other 4 because that's the other way to get 4. If you use 4 and 1, there is no way to get the -4x in the middle term. Therefore the factors are (x-2)(x-2) or (x-2)^2.

The last problem is 2x^2 - 3x - 2
The answer is (2x+1)(x-2)
Solve it the same way problem 3 was solved
If you practice factoring, it will become easier and easier for you.

Answer 3

If I am reading the problems correctly, the answers go a little something like this:

1. (2x + 1) (2x -1)

Check answer: 2x times 2x is 4x^2. 2x times -1 is -2x. 2x times 1 is 2x. 1 times -1 is -1. So the final results gives us: 4x^2 -2x + 2x -1 = 4x^2 - 1.

3. (x -2)(x-2)

Check answer: x times x = x^2. x times -2 = -2x. x times -2 = -2x. -2 times -2 = 4. so the final results are: x^2-2x-2x+4 = x^2-4x+4.

4. (2x + 1)(x-2)

Check answer: 2x times x = 2x^2. 2x times -2 = -4x. x times 1= x. 1 times -2 = -2. So the final results are: 2x^2 -4x +1x-2 = 2x^2-3x-2.

Answer 4

(2x+1)(2x-1)
4x^2+2x-2x-1 the 2x's cancel out cuz one is positive and the other negative which leaves you with 4x^2-1

follow this pattern to solve the others :)