How can factoring make the work in Exercises 21,22, and 67...

Key Concepts

Factoring

Factoring is the process of rewriting an expression as the product of its simpler components. In algebra, it is used to break down complex expressions, making them easier to work with by revealing common or underlying structures.

Common Factors

Identifying and extracting common factors from terms in an expression helps in consolidating the expression into a simpler form. This often reduces the effort required in performing operations such as simplification, evaluation, or solving equations.

Algebraic Simplification

Algebraic simplification involves using methods like factoring to reformulate expressions into reduced or more manageable forms. This simplification can make subsequent computations quicker and less error-prone.

Transcript

00:01 All right, in this video, they asked for how can factoring make numbers 21, 22, and 67 easier.

00:07 And i'm going to use a particular one and kind of show you how to do this.

00:10 So all of these right here, they have a relationship or something in common, is there all some of cubes, or at least in the numerator anyway? so we can use a factoring technique to kind of make the, i guess, essentially, the functioner sequence a lot smaller.

00:29 So we actually plug in numbers.

00:30 It's not so much, it's not so time -consuming.

00:32 So i'm going to work on, i'm sure you how to do this with the number 67, but it does work for the other two.

00:38 Okay, so the first you want to do is see what's actually being cubed.

00:41 So again, i'm just going to kind of focus on this right here for right now.

00:45 So the way i can rewrite this is that, again, each part, or at least the numer is being cubed.

00:50 So i can obviously x, subscript i is being cubed, but also can rewrite 1 ,000 as 10 cubed.

00:57 Okay? so what i can do now is use a factoring technique to break that down and then kind of show you how you can.

01:03 Make this function or sequence a little bit smaller or series smaller.

01:07 So the technique i use for factoring sum of cubes is the kind of notation here.

01:14 I call it sum us.

01:16 Okay, s stands for square.

01:20 O stands for opposite, m stands for multiply, a stands for add, oops, and the s also stands for square again.

01:32 Okay, and what this does, it helps you break down the trinole that you're bunch you're going to get.

01:37 So what's going to happen is you're going to break this into a binomial, a two -term expression times a trinomial, and this will help you with the trinomial.

01:45 Okay, but you need the binomial first.

01:47 Okay, so for the binomial, what you're doing, you're basically just take off the cube part to our expression we have right above it.

01:53 So we're going to do s, subscript i plus 10...

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