How does factoring work in algebra and why is it important for calculus?

[Deicider]

Homework Statement

Well,i never paid attention to maths,few things i learned and now i need to solve calculus(dont ask why) but to do that i need to first understand how factoring works,its a basic thing,yes ,i'v missed it and can't go on without it.
2. Relevant equations
Few examples and solutions from the book.
1) x^3-3x^2=x^2(x-3)
2) x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)
3) 4x^2-1=(2x-1)(2x+1)
4) x^3-x=x(x^2-1)=x(x-1)(x+1)

The Attempt at a Solution

I spent few hours to understand them by myself but couldn't.
Can anyone explain in details how exactly this works?
Help the newb.

 

[snshusat161]

x^3 = x multiplied by x multiplied by x
similarly x^2 is equal to x multiplied by x

so $$x^{3} - 3 x^{2} = x. x. x - 3. x. x$$

Take out what is common in between. Here common term is x.x
so x. x can be written as $$x^2$$

so it is equal to $$x^{2}(x-3)$$

And for all the rest, you have to know one formula

$$(x^{2} - a^{2}) = (x - a)(x + a)$$

Actually the your problem is so easy that it is difficult for me to tell. And I think that's the reason why nobody has answered it yet. I don't know how to explain such problems but I've tried my best.

 

[willem2]

Before you can think of factoring the expression of the left, you should know
how to multiply the factored expression on the right, to get the expression
on the left.

 

[Mark44]

Well,i never paid attention to maths,few things i learned and now i need to solve calculus(dont ask why) but to do that i need to first understand how factoring works,its a basic thing,yes ,i'v missed it and can't go on without it.

If you're studying calculus now, and are mystified by factoring, you've really got your work cut out for you. Realistically, you will probably need to spend half or more of your time brushing up on algebra and trig concepts in order just to be able to understand the work shown in examples. And that doesn't include being able to work the problems through from start to finish.

Some people can do this, and some can't, and this depends to a fair degree on their motivation or lack thereof. Unlike some other disciplines, success at one level of mathematics requires a solid understanding of the preceding subjects. You might be able to understand some of the calculus concepts at a high level, but if you can't factor expressions or do the other things that you are expected to have mastered, it's going to be very difficult.

 

[snshusat161]

I'm telling you my way of studying Maths. I never try to understand by looking at the examples. I start solving it, doesn't matter whether i know it or not. and when you'll stuck look at book to know how they had cleared that bump

 

[Char. Limit]

The reason why $$x^2-a^2=(x+a)(x-a)$$ is this:

Let's expand $$(x+a)(x-a)$$

$$(x+a)x-(x+a)a$$

$$x^2+ax-ax-a^2$$

$$x^2-a^2$$

Apply similar ideas to the rest.

 

[Deicider]

Am failure of digits ,a beggar of numbers ,am a dying equation ;(

Ok now,why maths are separated into pre and post calculus?
I just need to learn algebra first right?

 

[Mark44]

Am failure of digits ,a beggar of numbers ,am a dying equation ;(

Ok now,why maths are separated into pre and post calculus?
I just need to learn algebra first right?

Yes, and trigonometry as well. As I said before, in order to succeed in calculus, you first have to have the foundations in place.