Can you guys explain on how to expand & factorize algebraic expression in a simple way?

Give us an example and show us some work.
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As the other commenter said, examples of where you struggle would really help people provide feedback here. Show us a problem, your line of reasoning and proposed answer, and then the answer that you were told it actually was.

In general, factorizing can be quite difficult. There are basic things to check that you should get accustomed to. There are go-to theorems that give you a framework to work with when it's really tricky. But a lot of the time the key is having enough practice and experience with it that you spot neat tricks and shortcuts. That kind of thing is difficult to just hand someone without having them put the work in.
If you are talking about factoring quadratics, it's just trial and error (the other methods are complicated and not faster). Note that factoring here is a *shortcut*. If it takes you longer than a few seconds, just use the quadratic formula.

Anything higher power is just tricky. There are a few tricks you can memorize for cubics. But generally you should not expect to see it right away.

In either case, you can check your answer by expanding back out.

Expanding is just the distributive property. Don't bother with other explanations. Do you have an example that you can't expand?

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