# Algebraic calculation : Reminder

Algebraic calculus is a form of calculus that combines letters, numbers, and operations. The following formulas can be used in factoring and expanding algebraic expressions.

### Factoring and expansion

1. #### Formulas

2. Let a, b and k be three numbers we have :

• ka+kb=k*(a+b)
• ka-kb=k*(a-b)
To factor an algebraic sum is to turn it into a product. To expand is to turn it into an algebraic sum.

3. #### Special expansions

4. Let a,b be two numbers we have the following three equalities: :

These equalities are known as special expansions.

5. #### Factoring by (x-a)

6. P is a polynomial, a a real. If P(a)=0, then P is factorizable by (x-a). That is, there exists a polynomial Q such that for all x, P(x)=(x-a)Q(x).

### Reduction of a literal expression

To simplify a literal expression, we group the dependent terms depending on the same letters and then we reduce each grouping, as in this example: x+x+3y-2y=2x-y.