Factorise for Dummies

Factorise is a mathematical term that we use to describe the process of breaking down a number or an expression into its smaller parts or factors. It's like taking a big jigsaw puzzle and figuring out how all the individual pieces fit together to make the whole picture. When we factorise, we're trying to find those smaller pieces, or factors, that when multiplied together, give us the original number or expression.

Let's say we have the number 12. We can factorise it by finding its factors, which are the numbers that can be multiplied together to give us 12. In this case, the factors of 12 are 1, 2, 3, 4, 6, and 12. Now, we can think of these factors as the smaller puzzle pieces. If we arrange them in a certain way and multiply them together, we'll get the original number 12. For example, we can factorise 12 as 2 x 6 or as 3 x 4. Both of these sets of factors multiply together to give us 12.

Factorising can also be applied to algebraic expressions. Instead of numbers, we're working with variables and symbols. Imagine we have the expression x^2 - 4. We want to factorise it by finding the factors or smaller parts that can help us rewrite the expression in a simpler form. In this case, the factors of x^2 - 4 are (x - 2)(x + 2). When we multiply these factors together, we get back the original expression. It's like finding the missing pieces of our puzzle and putting them together to see the whole picture.

To sum it up, factorising means breaking down a number or expression into its smaller parts or factors by finding the numbers or variables that can be multiplied together to give us the original number or expression. It's like a puzzle-solving process where we search for the missing pieces and fit them in the right place to complete the picture. Whether we're dealing with numbers or algebraic expressions, factorising helps us understand the structure and relationships within them, making math problems more manageable and easier to solve.