What is the difference between simplify and factor

With practice this can be done mentally, provided the squares of integers up to about 20 are known. The difference of two squares can also be used to solve equations in which we only seek integer solutions.

These identities are harder to use than the difference of two squares and are probably best dealt with as special cases of quadratic factoring, discussed below. The following example shows how these ideas can be cleverly combined to factor an expression that at first glance does not appear to factor. At first glance this expression does not appear to factor, since there is no identity for the sum of squares.

However, by adding and subtracting the term , we arrive at a difference of squares. This expansion produces a simple quadratic. We would like to find a procedure that reverses this process. We notice that the coefficient x of is the sum of the two numbers 2 and 5 in the brackets and that the constant term 10, is the product of 2 and 5.

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. A single variable, like x, y, or z is also an expression. Expressions may also be more complex. An equation, on the other hand, is simply any two expressions that are set equal to one another.

Now, if you were asked to simplify an expression, that's asking you to rewrite the expression in a different form that's easier to work with. Factorizing is, in essence, a specific form of simplification, in which the expression is reduced to a form involving two or more factors.

And, finally, solving an equation is when you find the value s for which the equation holds true. In some cases, the answer may be "all real numbers," in which case you may see that equation referred as an "identity. This equation produces infinitely many solutions, yet they can be written compactly as one "family" of solutions. This equation is never true assuming real-valued m anyway , thus it has no solutions.

Thanks a lot for the detailed explanations. Click to expand Joined Oct 6, Messages 10, Some schools state this instruction as, "Make h the subject". If, instead, you know the radius, but you want to determine the height required to hold a specific volume, then you would use the red equation formula. Last edited: Sep 3, 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.

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.

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.

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 The resulting equation would be 6c