Factorization — taking out common factors: MYP 2 Mathematics Notes

Why Factorization Matters in Science

In science, we constantly work with formulas , equations that describe how quantities relate to each other. Many of these formulas can be simplified or rearranged using factorization, which is why this algebraic skill is so important in scientific work.

Analogy

Consider the formula for the total resistance of two resistors in a circuit: $R_{t o t a l} = I R_{1} + I R_{2}$ . A physicist would immediately spot that $I$ is common to both terms and write this as $R_{t o t a l} = I (R_{1} + R_{2})$ , that's factorization in action!

Here are some real scientific contexts where factorization appears:

Physics: Simplifying equations for force, energy, or motion (e.g. $F = m a_{1} + m a_{2} = m (a_{1} + a_{2})$ )
Chemistry: Working with molar quantities in reaction equations
Biology: Simplifying expressions for population growth or area calculations

In this subtopic, you will learn the technique of factorization , taking out common factors , so that you are fully equipped to handle algebraic expressions wherever they appear in your scientific studies.

What is Factorization?

You already know how to expand brackets , for example, $2 (x + 4) = 2 x + 8$ . Factorization is the reverse process: you start with an expanded expression and rewrite it in a compact, factored form.

Factorization: Factorization is the process of rewriting an expression as a product of its factors. It is the reverse of expanding brackets.

Factored Form: An expression is in factored form when it is written as something multiplied together, for example $3 (2 a + 3)$ .

Analogy

Think of factorization like unpacking a parcel. Expanding is packing items into a box (multiplying out). Factorizing is opening the box and reading the label , the label on the outside tells you the common factor, and the contents list inside tells you what remains in the bracket. Together, they multiply to give you back the original expression.

Because expanding means multiplying, it is natural that factorizing involves dividing , you divide each term by a common factor and place that factor outside the brackets.

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