Expanding vs Factoring

Mathematics is a major subject present throughout primary, secondary, and even tertiary education. However, not all people are good at math for a number of reasons. The foremost reason is that people don’t realize that mathematics, like any other skill, must be practiced in order to be perfected. Problem solving is similar to learning how to drive: one has to spend a lot of hours in the driver’s seat in order to gain a thorough understanding how the car controls work. In the same way, one has to do a lot of problem solving, master different formulas, and learn the definition of mathematical terms in order to excel in Mathematics. No matter how naturally gifted one is at Mathematics, an incomplete or incorrect understanding of mathematical terms can still lead to failure. Most problems in algebra, geometry, and trigonometry can be solved if one knows how to manipulate formulas, at the same time knowing how to define and differentiate between mathematical terms. One’s understanding of how a formula works, or what a term stands for, can make the difference between a passing or failing score in any Mathematics subject.

Expanding and factoring are two commonly used terms in Mathematics. However, not everyone can tell the difference between them. Most people would simply say that both terms have something to do with removing or adding parentheses in an algebraic equation. But they won’t be able to give a clear example of how a certain equation is expanded or factored out.

In order to know the difference between the two terms, let us utilize the two equations. The first equation would be expanded, while the second would be factored out. How does one expand the equation: 2(3c-2)? First, take note of the parentheses present in the equation. Expanding the equation means removing the parentheses. In order to derive a parentheses-free equation, one simply multiplies the value outside the value, which is 2, to each of the values inside the parentheses. This means that 2 is multiplied to 3c, and 2 is also multiplied to -2. The resulting equation would be 6c-4. Since the equation has no more parentheses, it is said to be completely expanded.

If expanding means removing parentheses, then factoring out is the opposite, because it means adding parentheses to an equation. How does one factor out the equation xy + 3x? First, one takes into consideration the common variable between the two values, which is x. The remainder of the equation, which is y + 3, is enclosed in parentheses. The factored-out version of the equation xy + 3x is x(y+3).

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.

Summary:

1. In order to excel at mathematics, one should have a thorough grasp of formulas and mathematical terms.

2. 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.

3. 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.

4. 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.

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