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.