# Algebra - Explanation and Worked Examples on Algebra

### Concept of Algebra:

Consider this simple statement:

I am a number. When you subtract 3 from me, the result is 9. what number am I?

Of course we know the answer is 12. You probably guessed it from your mind because it was that simple. The truth is, We could have a much more complicated statement of such; and that is where algebra comes into play.

Now, to apply algebra in the above statement, we use letters or alphabets to represent the unknown number(s). So using algebra, we can write:

• Let the number be y

• y - 3 = 9

• y = 9 + 3

• y = 12

#### So why is it easier using letters?

if we had a question of several unknowns, the question can become complicated, hence using letters can actually make things easier for us.

To simplify a mathematical expressions, we need to represent them in the least complicated form as much as we can, making them more easier to work with.

One skill you need to know is the combination of 'like terms'.

Like terms refers to those variables that are exactly the same, although they may still have different coefficients. Understand that coefficients always precedes a variable. This is explained in the instance below.

• 5a2 and 12a2 are considered to be like terms because the have the same variable a2. The coefficients in this instance are 5 and 12 respectively.
• 3ab and 3bc are not like terms because the have different variables (ab and bc) with coefficients (3 and 3) respectively.

In order to combine the like terms, we will have to add or subtract them (depending on the given sign) so that we can have a single term.

### Worked Examples

Example 1:

• Simplify 10ab + 7ab
• Since '10ab' and '7ab' are like terms, that is, they both have the same variable (ab), we will add their coefficients together in order to get our answer
• (10 + 7)ab = 17ab

Example 2:

• Solve y2 + 5 + 7y2 - 5y + 10
• First, let's combine the like terms. Understand that a variable without a coefficient in front of it is always assigned the value of 1. Also, when moving coefficients, we should take into account the '+' and '-' values in front of them.
• (1 + 7)y2 - 5y + (5 + 10)
• Answer is 8y2 - 5y + 15

Example 3:

• Solve 4b + 4 = 20
• Step 1: Let's move over like terms. When a like term is moved over the '=', the '+' value before it changes to '-'. If the like term has '-' value in front of it, then it turns to a '+'.

• 4b = 20 - 4
• 4b = 16
• Step 2: To get b, we will need to divide both side by b's coefficient which is 4.

• 4b/4 = 16/4
• Answer is -> b = 4

Example 4:

• Solve 4a + 5 = 2a - 1
• Step 1: Let us move the like terms

• 4a - 2a = -1 - 5
• 2a = -6
• Step 2: Let's divide both sides by a's coefficient which is 2).

• 2a/2 = -6/2
• Answer is -> a = -3

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