I can not figure out how to factor this problem?

Question

1-16x^4

Answer 1

You have a difference of squares.

In general if you have a² - b², that is equivalent to (a+b)(a-b). Multiply it out if you aren't sure. You'll see that you get a² -ab + ab + b² and the +ab and -ab cancel out.

In your example you have:
1 - 16x^4

This is equivalent to:
1² - (4x²)²

Using the rule above:
(1 - 4x²)(1 + 4x²)

Next notice that you have another difference of squares:
(1² - (2x)²)(1 + 4x²)

Again using the rule, you can split the difference of squares:
(1 - 2x)(1 + 2x)(1 + 4x²)

Unfortunately you can't do much else with the 1+4x², so your expression is fully factored.

Answer 2

a^2 - b^2 = (a-b)(a+b)

1-16x^4 = (1 - 4x^2)(1 + 4x^2)
=(1-2x)(1+2x)(1+4x^2)

Answer 3

a² - b² = (a+b)(a-b)

1 - 16x^4
= 1² - (4x²)²
= (1+4x²)(1-4x²)
= (1+4x²)(1-(2x)²)
= (1+4x²)(1+2x)(1-2x)

Answer 4

(1+4x^2)[(1-2x)(1+2x)]

difference of two squares

hope this helps

Answer 5

(1-16x^4)
=1-(4x^2)^2
=(1-4x^2)(1+4x^2)
=(1-2x)(1+2x)(1+4x2)