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

Formulas

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.

Special expansions

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

• `(a+b)^2=a^2+2*a*b+b^2`
• `(a-b)^2=a^2-2*a*b+b^2`
• `(a-b)*(a+b)=a^2-b^2`

These equalities are known as special expansions. Here is an example of using remarkable identities to factorize an algebraic expression: