Learn Basic Algebra: Questions, Problems and Help

Algebra Basics

Factors

Finding factors and using them in equations is one of the common activities in algebra class. Factors are the numbers that can be multiplied together to create another number. For example, you can get the number eight by multiplying 4 x 2 and 1 x 8, so the factors of eight include the numbers one, two, four and eight. Even prime numbers, like seven, have factors because 1 x 7 = 7.

Finding Common Factors

Sometimes in algebra, finding the factors that two numbers have in common can help you solve an equation. Let's find the common factors for 25 and 30. All the numbers that can be divided by 25 to reach a whole number are one, five and 25, because 5 x 5 = 25 and 25 x 1 = 25. The number 30 can be divided by one, two, three, ten, five, six, 15 and 30. This is because 2 x 15 = 30, 5 x 6 = 30, 3 x 10 = 30 and 30 x 1 = 30. So, the common factors of 25 and 30 include one and five. The greatest common factor (GCF) is five.

FOIL Method

You will eventually encounter complex equations that you must simplify. To do this, you can use the first, outer, inner and last (or FOIL) method.

Let's simplify this expression: (4x + 2)(3 + 9). The FOIL method tells us that we must multiply the first terms from each parenthesis, which are 4x and three (4x * 3 = 12x). Next, we must multiply the outer-most terms, in this case 4x and nine (4x * 9 = 36x). Now, we calculate the inner numbers (2 * 3 = 6). The final letter in FOIL tells us to multiply the last numbers: 2 x 9 = 18.

Now the expression becomes 12x + 36x + 6 + 18. Simplify by combining like terms.

'Like terms' are terms of algebraic expressions that have the same variables. Because six and 12 are both integers with no attached variable, they can be added together to simplify the expression to 12x + 36x + 24.

Now you can further simplify by combining 12x and 36x, which are also like terms because they both have an x variable. The final simplified expression should look like this: 48x + 24.