Is it factorable?

Question

Must be factored by the difference of squares
(a+b)(a-b)=a^2 - b^2

4x - 36x^ 3

also try

8x^2 - 32y^2

Answer 1

Of course it is!
Look:
4x-36x^3
4 and x is common between the both of them.
4x (1-9x^2)
Then because 1^anything would still equal to 1, 9 root is 3, x^2 root is x.
4x(1-3x)(1+3x)
So there you go.
Then moving on to the other one.
8 is the only thing they have in common, so
8x^2-32y^2
=8(x^2-16y^2)
So like the one above, 4 squared in 16, and y^2 root is y.
Then you would get:
8(x-4y)(x+4y)
There you go, both of them used the a^2-b^2 formula, you just have to learn to see the pattern and it may be sometimes concealed by multiplying both of the numbers.

Answer 2

Yes, it is.
For the first expression:
First, to put the first equation into the a^2-b^2 form, you have to factor out an x. So:
4x-36x^3 = x(4-36x^2)
Now, we deal with the stuff inside the paranthesis. the square root of 4 is 2 and the square root of 36 is 6. So you have:
x(2+6x)(2-6x) as your final answer.

For the second expression:
First, in order to make the coefficients perfect squares, you need to factor out a 2. So:
8x^2-32y^2= 2(4x^2-16y^2)
Then, using the same method as in the first one, you factor so you get:
2(2-4x)(2+4x) as your final answer.

I hope I could help!

Answer 3

First, extract x to get
x(4-36x^2)
The right factor is a difference of squares
x(2-6x)(2+6x)
If you as extracted 4x, then
4x(1-9x^2)
4x((1+3x)(1 - 3x)

8x^2 - 32y^2 = 8(x^2 - 4y^2) - recognize the squares...
8(x+y)(x - y)

Answer 4

The directions don't say factor completely. They say only to factor using the difference of squares. Both of these expressions are directly factorable into the sum and difference of two numbers without extracting any other factors first.

4x - 36x^ 3 = [2x^(1/2)+6x^(3/2)][2x^(1/2)-6x^(3/2)]

8x^2 - 32y^2 = [2(sq rt 2)x+4(sq rt 2)y][2(sq rt 2)x-4(sq rt 2)y]

Answer 5

4x - 36x^3 = 4x (1 - 9x^2) = 4x (1 + 3x) (1 - 3x)

8x^2 - 32y^2 = 8 (x^2 - 4y^2) = 8 (x + 2y)(x - 2y)

Answer 6

4x - 36x^ 3
=4x(1-9x^2)
=4x(1-3x)(1+3x)

8x^2 - 32y^2
=8(x^2-4y^2)
=8(x-2y)(x+2y)

Answer 7

4x - 36x^ 3 = 4x(1^2 - (3x)^2) = 4x(1 - 3x) (1 + 3x)

8x^2 - 32y^2 = 8(x^2 - (2y)^2 ) = 8(x-2y)(x+2y)

Answer 8

4x(x+6)(x-6)

2.8(x+2y)(x-2y)