Factorization of Expressions - JSS3 Mathematics Lesson Note

I. Factorization of Expressions

1. Factorization of 𝑎𝑥+𝑎𝑦

When you have an expression like 𝑎𝑥+𝑎𝑦, you can factor out the common factor 𝑎:

𝑎𝑥+𝑎𝑦=𝑎(𝑥+𝑦)

Example:

2𝑥+2𝑦=2(𝑥+𝑦)

2. Factorization of 3𝑚+𝑝𝑞+3𝑝+𝑚𝑝

Here, we look for common factors or grouping:

3𝑚+𝑝𝑞+3𝑝+𝑚𝑝=3(𝑚+𝑝)+𝑝𝑞

Example:

3𝑚+2𝑝𝑞+3𝑝+𝑚𝑝=3(𝑚+𝑝)+2𝑝𝑞

3. Factorization of 𝑎^2−𝑏^2

This is a special case known as the difference of squares, which factors as:

𝑎^2−𝑏^2=(𝑎−𝑏)(𝑎+𝑏)

Example:

9𝑥^2−4=(3𝑥−2)(3𝑥+2)

4. Factorization of 𝑎^2−2𝑎𝑏−𝑏^2

This expression can be factored using a pattern for a quadratic form:

𝑎^2−2𝑎𝑏−𝑏^2

=(𝑎−𝑏)^2−2𝑎𝑏a 

Example:𝑥^2−2𝑥𝑦−𝑦^2

=(𝑥−𝑦)2−2𝑥𝑦