factoring problem

[tuhlmeyer]

Can someone please show me how to factor this equation?

x¹² - 729

The answer to the equation is (x²-3)(x⁴ + 3x² + 9)(x² + 3)(x^{4 _} 3x² + 9)

Thanks

 

[Mrspi]

Can someone please show me how to factor this equation?

x¹² - 729

The answer to the equation is (x²-3)(x⁴ + 3x² + 9)(x² + 3)(x^{4 _} 3x² + 9)

Thanks

What you have is NOT an equation; it is an "expression". To be more precise, this expression is a "binomial."

You have probably been studying factoring patterns, and at least a couple of those patterns involve factoring some special kinds of binomials.

One special polynomial is a difference of two squares. The general form for a difference of two squares and its factorization is

a² - b², which factors into the product of two binomials of the form (a + b)(a - b).

You have a DIFFERENCE of two terms. Are those terms, perhaps, SQUARES of something?

Well, x¹² can be thought of as (x⁶)². Oh! And look at 729....that's a square too! 729 is 27².

So you CAN think of this as a difference of two squares:

(x⁶)² - 27²

That should give you something to start with, at least. Show us how you would factor this using the difference of two squares pattern, and we can go from there.

 

[Deleted member 4993]

In addition, you should know:

a³ - b³ = (a - b) * (a² + a*b + b²) and


a³ + b³ = (a + b) * (a² - a*b + b²)