What is the difference between factorisation and expansion

Factorisation is basically the reverse method for expansion. Factorisation is mostly used when solving algebraic equations. I feel that this topic is is not as difficult as it looks like. In the beginning I was quite confused however, once I got the hang of it, I could expand and factorise quadratic expressions with ease.

I also feel that we have to be extra careful and patient while solving quadratic expressions as it can be tricky and the possibility to make careless mistakes is quite high. This topic can be very useful while creating expression when solving word problems.

In conclusion, I would like to say that I enjoyed learning this topic. Menu Skip to content Home About. Search for:. This usually occurs when a term outside a bracket is multiplied by every term inside the bracket. The outside term "distributes" itself over the inside terms. Thus the name the distributive property. When an expression is expanded, each term inside the bracket is multiplied by the term outside the bracket.

If expanding means removing parentheses, then factoring out is the opposite, because it means adding parentheses to an equation. First, one takes into consideration the common variable between the two values, which is x. Now that the difference between the two terms has been explained, one understands how important it is to know the exact definition of mathematical terms.

Knowing how to expand or factor out an equation helps greatly in problem solving. It also enables one to not only solve equations, but also explain objectively the difference between two mathematical terms. In order to excel at mathematics, one should have a thorough grasp of formulas and mathematical terms.

Two commonly used mathematical terms, expanding and factoring, have one thing in common: they deal with either the addition or removal of parentheses in an algebraic equation.

Expanding an algebraic equation means getting rid of the parentheses. In order to remove the parentheses, the value outside the parenthesis is multiplied to each of the values inside the parentheses. On the other hand, factoring out an algebraic equation means adding parentheses to the equation.

This is accomplished by taking out the most commonly used value in an equation, then isolating the remaining values in parentheses. Cite APA 7 Franscisco,. This suggests a method of factoring. Hence to reverse the process, we seek two numbers whose sum is the coefficient of and whose produce is the constant term. Clearly the solutions are 4 and 3 in either order , and no other numbers satisfy these equations. Students should try to mentally expand to check that their answers are correct. Also note that the difference of squares factorisation could also be done using this method.

This is, however, not a good method to use. It is better for students to be on the look out for the difference of squares identity and apply it directly.

Students will need a lot of practice with factoring quadratics. It is worth mentioning here that in further mathematics, both in the senior years and all the way through tertiary level mathematics, quadratic expressions routinely appear and so being able to quickly factor them is a basic skill.

We should always be on the look out for common factors before using other factoring techniques. We can then proceed to factor further. There are a number of different techniques for factoring this type of expression.

The one presented here is felt to be the easiest both to perform and explain. It also links in with the techniques discussed above. It does not matter in what order we write the middle terms, the method will still work, thus. Simplifying algebraic expressions. We will now apply the various techniques of factoring to simplify various algebraic expressions. Students must take great care when cancelling. Factorising also can assist us in finding the lowest common denominator when adding or subtracting algebraic fractions.

Factoring quadratics provides one of the key methods for solving quadratic equations. Equations such as these arise naturally and frequently in almost every area of mathematics.

The method of solution rests on the simple fact that if we obtain zero as the product of two numbers then at least one of the numbers must be zero. The method of factoring non-monic quadratics can similarly be used to solve non-monic quadratic equations.