How do you know when to rewrite square trinomials and difference of squares binomials as separate factors? How can sums and differences of cubes be identified for factoring?

A trinomial is an expression that has three terms.

Square trinomial

A square trinomial is simply a perfect square trinomial, and it is represented as:

Difference of square binomials

This is easily identified because, the terms of the square binomials are perfect squares.

The difference of square binomials is represented as:

Sums and difference of cubes

When cubes are added or subtracted, they can be expressed using the following

--- sum of cubes

--- difference of cubes

Read more about binomial and trinomial at:

link

I answered most of your question below

Step-by-step explanation:

Well in basic high school math, you prolly will never HAVE to factor square binomials. It becomes more of an issue when you take the limit, and there is a zero in the denominator and blah blah.

But to answer your question. You can pretty much factor any trinomial with the basic rule. Sometimes youll have to complete the square because the trinomial wont be factorable until then. The main use of factoring trinomials tho is to find the value of x. Most trinomials usually equal 0 when youre in high school math. So you factor and make both equations equal 0. Another case where you might need to factor is when you are dividing a trinomial by a binomial. You can factor the numerator and denominator and potentially cross out two terms that divide to equal 1. Overall, its really helpful.

I never really felt the need to actually factor square binomials. Its the thing like a^2 - b^2 = (a + b)(a - b), right? Its basically the same thing with what i said about the dividing stuff. One of those terms might be the exact same as one of the terms from the factored trinomial. Then you can cross out two entire terms