Expanding brackets and factorizing expressions |
Expanding BracketsExpanding brackets is actually much easier than most people think. To expand brackets such as a(b + c), all you have to do is multiply the term outside the bracket by everything inside the bracket (e.g. 2x(x + 2) = 2x2 + 4x). That being said, if we had an expression in the form of (a + b)(c + d), we could expand it into ac + ad + bc + bd, by multiplying everything in the first bracket by everything in the second. Example: Expand (2x + 2)(x - 3): (2x + 2)(x - 3) = 2x2 - 6x + 2x - 6 = 2x2 - 4x - 6 FactorizingFactorizing is a little tricky if you are not used to it, but that is not to say that it is difficult, you just have to get used to it. As a matter of fact it is very easy as you will see bellow. Factorizing is the reverse of expanding brackets, in other words, it is putting 2x2 - 4x - 6 into the form (2x + 2)(x - 3). If you remember we used this in the posting Quadratic equations The first step in factorizing an expression is to take out any common factors which the terms have. So if you were asked to factorize x2 + 2x, since x is in both terms, you would write x(x + 2) . |
RELATED ARTICLES:
Evaluating Algebraic Expressions - BODMAS
When evaluating algebraic expressions, you will need to follow the right order of operations in order to get the right answer. In this posting we will cover the approach we call BODMAS - which denotes the order inwhich operators are applied: BODMAS stands for (Brackets -> Or
PL/SQL expressions and Boolean operators
Expressions are part of PL/SQL that evaluates to something, but is not valid on its own. For example, an expression can appear on the right hand side of an assignment operator, but that expression can not be used on its own, it has to e part of another statement. For example, 2
Quadratic Equations
Quadratic equations are polynomial equations of the second degree. This means that at least one occurrence of the variable (x) in the equation is raised to the power of 2. The general format for a quadratic equation is: ax2 + bx + c = 0 where x is the variable,
Solving Quadratic equations
In the posting Quadratic equations, we covered the quadratic equation formula, and how to solve quadratic equations. This posting is aimed at giving you more detail and perhaps a practical example of how to solve and graph a quadratic equation. To start with we take the...
Quadratic Formula
Constructing Quadratic equations from their answers
So far we have solved both linear and quadratic equations. This was done by using the quadratic equation formula, factorizing or by simply solving for a variable in a linear equation. What if the question in the exam was not to solve a quadratic equation, but rather to rec
Solving problems with Algebra
It is widely known that algebra is used to solve real-life problems by finding what is known by using what is known about the situation. Some mathematics students call this plugging in numbers. For example, consider the following problem: Kashamba drives x kilometers in 50