Can someone please explain factoring to me?

[Alzebra]

I understand most of Algebra except factoring. I don't understand how "canceling out" really works. Can someone please explain?

[stapel_eliz]

I understand most of Algebra except factoring. I don't understand how "canceling out" really works. Can someone please explain?

What do you mean by "canceling out" in factorization? (I'm familiar with cancelling factors to simplify fractions, but that's a separate process from the factorization, and is in a different context.)

Providing an example from your text or your class notes would be helpful. Thank you!

[Alzebra]

Here is one of my problems that I am struggling with:

FACTOR x to the 4th power - 9y squared

Then is says "1. x to the 4th power = (x squared) squared, and 9y squared = (3y) squared." I understand that.

And then it says "2. x to the 4th power - 9y squared = (x squared) squared - (3y) squared." I understand that, too, because I just said those were equal.

THEN, suddenly, it says it says, "3. And so, x to the 4th power - 9y squared = (x squared + 3y)(x squared - 3y). Solved"

WHERE did that come from??? Can someone please explain why (x squared) squared - (3y) squared turns into (x squared + 3y)(x squared - 3y)???

[stapel_eliz]

THEN, suddenly, it says it says, "3. And so, x to the 4th power - 9y squared = (x squared + 3y)(x squared - 3y). Solved"

WHERE did that come from???

From factoring the difference of squares.

They applied the formula that should have been covered in class; check that section, or a section or two previous, to find the formula in your book.

[Alzebra]

Thanks, stapel_eliz. I looked at that formula, and I think I understand it. I geuss I just skipped it by accident in my book. Thank you!