Santa Rosa Junior College Mathematics Gale Bach Beginning Algebra Math 151 Fall 2017 http://profiles.santarosa.edu/gale-w-bach

Why Math?

What is Math?

What is Math?

Examples of Algebraic Expressions 5 + 7 6x2 + 7x2 19xy – 30xy + 8 13xy2 – 7x2y + 11xy2

A term is a number, or the product of a number and variables raised to powers – (the number is called the numerical coefficient). Examples of Terms 7 (numerical coefficient is 7) 5x3 (numerical coefficient is 5) - 4xy2 (numerical coefficient is - 4) z2 = 1 z2 (numerical coefficient is 1)

Like terms contain the same variables raised to the same powers. To combine like terms, add or subtract the numerical coefficients (as appropriate), then multiply the result by the common variable factors.

Examples of Combining Terms Terms Before Combining After Combining Terms 5 + 7 6x2 + 7x2 19xy – 30xy + 8 13xy2 – 7x2y + 11xy2 12 13x2 – 11xy + 8 24xy2 – 7x2y Simplified Algebraic Expressions

Example: Find each product by using the distributive property to remove the parentheses. a.) 2(x + y) b.) 7(x + 2y – 5z) c.) – 4(3a – 3b – 10c) a.) 2(x + y) = 2x + 2y b.) 7(x + 2y – 5z) = 7x + 14y – 35z c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c

Examples a. b.

Example Formulas can be found in Appendix of your textbook.

Example Balanced