factorise a^12x^4-a^4x^12
you have common factors (ax)^4. Take that out of each term. Then, the second term is the difference of two squares (a^4)^2 - (x^4)^2, that can be factored, which leads to another difference of two squares, factor, and finally, another difference of two squares.
To factorize the expression a^12x^4 - a^4x^12, we can use the difference of squares factorization technique.
Step 1: Identify the common factors.
In this expression, we can see that both terms have common factors of a^4x^4. So, we can factor out a^4x^4.
a^12x^4 - a^4x^12 = a^4x^4(a^8 - x^8)
Step 2: Apply the difference of squares formula.
The expression (a^8 - x^8) is a difference of squares because it can be written as (a^4)^2 - (x^4)^2. According to the difference of squares formula, the difference of squares (a^2 - b^2) can be factored as (a - b)(a + b).
Therefore, we can factorize (a^8 - x^8) as (a^4 - x^4)(a^4 + x^4).
So, the fully factorized expression is:
a^12x^4 - a^4x^12 = a^4x^4(a^4 - x^4)(a^4 + x^4)
And that's how you factorize the expression a^12x^4 - a^4x^12.