Factorization — grouping and middle term splitting

Before we dive into specific techniques, let's make sure we understand what factorization actually means.

Factorization: The process of writing an algebraic expression as a product of two or more factors. It is the reverse of expanding (multiplying out) brackets.

Think of factorization as the opposite of expansion:

• Expanding: $3(x+2)=3x+6$
• Factorizing: $3x+6=3(x+2)$

When we factorize, we are asking: "What was multiplied together to give me this expression?"

In this subtopic, we'll learn two powerful factorization techniques:

1. Factorization by grouping
2. Middle term splitting (for quadratic trinomials)

Before learning grouping and middle term splitting, you need to be confident with the most basic factorization skill , taking out a common factor.

Common Factor: A number, variable, or expression that divides every term of the expression exactly.

To take out a common factor:

1. Identify the highest common factor (HCF) of all terms.
2. Write the HCF outside brackets.
3. Divide each term by the HCF and write the results inside the brackets.

Quick self-check: Try these before moving on.

• Factorize $4x^2+8x$ → Answer: $4x(x+2)$
• Factorize $15a^{2}b-10a{b}^2$ → Answer: $5ab(3a-2b)$

If either of those felt tricky, pause and review common factors before continuing , everything that follows builds on this skill!