Evaluating An Expression When A Value Is Given for The Variable

Math A-100 IUSB Sec 1.8 detailed notes – Week 2 Evaluating an expression when a value is given for the variable Example 1: simplify: 5x 2 when x = 4 Put 4 in for x: 5(4) 2  5(16)  80 Term s - each different way a value is shown, can be a number, one or more variables, or a combination of a number and variables, can have exponents but don ’ t have to Classes of terms: Like terms : 1) have the same variables, i.e. exactly the same letters 2) the exponents on those variables must be the same 3) the constant can be different though 4) can be combined, i.e. either added together or subtracted Examples: 4xy 2 z 3 & - xy 2 z 3 are like terms -9 & 74 are like terms Unlike terms – have different variable and/or different exponents on those variables Examples: 4xy 2 z 3 & - xyz 3 are unlike terms -9x & 74 are unlike terms Like terms vs Unlike terms Like terms can be put together, or combined, using addition and subtract. Unlike terms , since they are different than each other, cannot be. (if you go to a fast food restaurant and order 3 super burgers, 4 cheeseburgers, and 6 hamburger, you don ’ t expect to be given 13 plain hamburgers). So, if you haver like terms , then add or subtract them as indicated and bring any other unlike terms along for the ride. Example 1: Combine the like terms: 2x – 5y + 6x – 7y + 9x 2 Rearrange the terms to put the like terms next to each other: 2 x + 6 x – 5 y – 7 y + 9 x 2 “ collect ” the like terms (a.k.a. simplify by adding/subtracting the like terms together) 8 x – 12 y + 9 x 2 NOTE : we usually write polynomials in “ standard form ” , i.e. the terms are written with the variables in alphabetical order and with the highest degree (i.e. exponent) first. So, the proper answer here is

9 x 2 + 8 x – 12 y NOTE : we cannot combine the 9 x 2 with the 8 x because they are NOT like terms (double cheeseburgers are not the same as single cheeseburgers). Example 2: Combine the like terms: 12xy – 3y 2 - 4x + 7y + 9x 2 - 2xy – 13y 2 - 8x - y + 11x 2 Rearrange the terms to put the like terms next to each other: 9x 2 + 11x 2 - 4x - 8x + 12xy - 2xy + 7y - y – 13y 2 – 3y 2 “ collect ” the like terms (a.k.a. simplify by adding/subtracting the like terms together)