Factorization of Algebraic Expressions

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Introduction to Factorization of Algebraic Expressions

The most common question asked by students when they are faced with algebra problems is how does it apply to their everyday lives? The fact of the matter is that algebra is abstraction and largely a mathematical tool. However, the habit of approaching problems systematically and methodically is what essentially translates to problem solving abilities in real life.

The Big Idea: What is factorisation of algebraic expressions?

When we examine the number 12, we know that it is the product of 2 x 2 x 3, which means that these are the prime factors of 12. This process can be called the prime factorisation of 12, where it has been broken down into its smaller components. Similarly, it is possible to break down an algebraic expression into its smaller components for simplification. This is called factorisation of algebraic expressions.

If described in another way, factorisation of an algebraic equation can also be more simply described as the process of finding what needs to be multiplied together to get that expression.

Why is the factorisation of algebraic expressions important?

This process of simplifying an algebraic equation is very important. It helps you to reach the solution faster. You do not need to go through humongous calculations to reach the solution. The chances of errors in calculation are therefore minimized because there are fewer calculations to be done, and the complexity of those calculations is reduced.

Factorisation based on common terms

The purpose of this method of factorisation of algebraic expressions is to find out what is common in two or more terms of the algebraic expression. For example, if an algebraic expression is written as \({(2x + xy),}\) then you can see that \({x}\) is common to both the terms. That is why this algebraic expression can also be written as \({x(2 + y)}\), which you can get by taking out the common factor. If you are later given values of \({x}\) and \({y}\), then factorisation would help you to multiply the value of \({x}\) only once.

Factorisation based on grouping

In the earlier method, we took out common factors from all the terms of the algebraic expression. But sometimes it is more convenient to divide the expression into convenient groups. This will be easier to understand with an example.

Now that you are armed with the concepts, let’s try solving some problems:

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