Algebra practice part 1

A. Operations with algebraic expressions

What is an algebraic expression? An expression combining numbers, possibly represented by symbols (x, y, S, T,…) combined by any or all of the operations of addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

A. Operations with algebraic expressions What is an algebraic expression? Example: is an algebraic expression in the variable x is an algebraic expression in the variables x and y is not an algebraic expression: it is an equation.

A. Operations with algebraic expressions Adding and subtracting algebraic expressions Example: Method: Work out the brackets Combine similar terms (terms that only differ by their numerical coefficients)

A. Operations with algebraic expressions Multiplying algebraic expressions: distributive properties Formulas: Example: This step mostly is not written explicitly

A. Operations with algebraic expressions Multiplying algebraic expressions: product of powers with the same base Example: Rule: product of powers with the same base Exercise:

A. Operations with algebraic expressions Multiplying algebraic expressions: special products Square of a sum / difference: Product of sum and difference: Exercises: (1) (2)

A. Operations with algebraic expressions Removing grouping symbols (brackets) Example: Method: Work out the brackets, from innermost towards the outside Combine similar terms

A. Operations with algebraic expressions Reference E.F. Haeussler, R.S. Paul, R.J. Wood: Introductory Mathematical Analysis for Business, Economics and the Life and Social Sciences Prentice Hall (Thirteenth edition) (shortened in what follows as “handbook”)

A. Operations with algebraic expressions Handbook Chapter 0: Review of Algebra 0.2 Some properties of Real Numbers 0.4 Operations with Algebraic Expressions (except: Long Division, p17)

B. Factoring

What is factoring? Writing an expression as a product of its factors Example: (Check!)

B. Factoring Method 1: factor out a common factor Example:

B. Factoring Method 2: factor by grouping Example:

B. Factoring Method 3: special formulas Square of a sum / difference: Product of sum and difference:

B. Factoring Handbook Chapter 0: Review of Algebra 0.5 Factoring (Except: Factoring trinomials, p19)