Please help with Factorising! I am very confused because I have been away from school. I am very confused with factorising with group terms and finding the HCF binomial factor and takin out the HCF.

try reading here:

http://www.mathsisfun.com/algebra/factoring.html

Location Elevation(ft)

Mt. Driskill 535
New Orleans -8

The table shows the highest and lowest elevations in Louisiana. What is the difference between the elevations?

what is the difference between 6 and 10?

How did you find it?

Do the same step with the numbers above

recall how to subtract negative numbers:

10 - (-5) = 10+5 = 15

No problem! I can definitely help you with factorizing. Let's start with factorizing by grouping terms.

Factorizing by Grouping Terms:
1. Check to see if there is a common factor in each pair of terms. If so, factor it out.
2. Within each pair, look for terms that have a common factor or expression.
3. Group those terms together and factor out the common factor.
4. If you can still factorize within each group, continue with the process until you can no longer factorize.

Here's an example to help illustrate the steps:
Let's say we have the expression: 4x + 8y + 3x + 6y

1. First, we check if there's a common factor for each pair of terms. In this case, there's no common factor for the first pair (4x and 8y), but there is a common factor 'x' for the second pair (3x and 6y).

2. Next, we group the terms that can be factored together. So, we group the first pair (4x and 8y) and the second pair (3x and 6y).

Our expression now looks like this: (4x + 8y) + (3x + 6y)

3. Now, within each group, we factor out the common factor. From the first group, we can factor out '4' as the common factor. From the second group, we can factor out '3x' as the common factor.

Our expression becomes: 4(x + 2y) + 3x(y + 2y)

4. We can see that we can still factorize within each group. For the first group, there's no further factorization possible. In the second group, we can factor out 'y' as the common factor.

Our fully factored expression is: 4(x + 2y) + 3xy(y + 2)

Now, let's move on to finding the Highest Common Factor (HCF) binomial factor and taking it out.

Finding HCF Binomial Factor and Taking It Out:
1. Given an expression, determine if there is a common factor that can be factored out.
2. To find the HCF binomial factor, identify terms that have a common factor or expression.
3. Once you've identified the HCF binomial factor, factor it out by dividing each term in the expression by it.

Here's an example to walk you through the process:
Let's say we have the expression: 5x^2y + 10xy^2 - 15x^3y

1. First, we look for a common factor that can be factored out. In this case, '5xy' is the common factor in all three terms.

2. The HCF binomial factor is '5xy'.

3. Finally, we divide each term in the expression by the HCF binomial factor '5xy' to factor it out.

Our factored expression becomes: 5xy(x + 2y - 3x^2)

I hope this explanation helps you understand factorizing with group terms and finding the HCF binomial factor. If you have any additional questions, feel free to ask!