Expressions Expressions Simplifying expressions means to combine like

Expressions

Expressions Simplifying expressions means to combine like terms by adding, subtracting, multiplying or dividing. Simplify the expressions.

Evaluate Expressions

Distributive Property The distributive property means to multiply terms. In a problem like, 4(x +2), you would distribute t(he 4 to the terms inside the parentheses and distribute means multiply. Examples of using the Distributive Property: multiply the number outside the parentheses by the terms inside the parentheses. a. 2(a + 4) : distribute the 2 to the a and the 4 or multiply 2 by a and 4, 2 x a is 2 a and 2 x 4 is 8 so the answer is 2 a + 8. b. 3(a – b) : distribute the 3 to the a and the –b or multiply 3 by a and –b, 3 x a is 3 a and 3 x –b is -3 b so the answer is 3 a – 3 b or 3 a + -3 b. c. a(b + c) : distribute the a to the b and c or multiply a by b and c, a x b is ab and a x c is ac so the answer is ab + ac. d. 3(2 x – 4): distribute the 3 to the 2 x and -4 or multiply the 3 by 2 x and -4, 3(2 x) is 6 x and 3(-4) is -12 so the answer is 6 x -12. e. -3(2 x – 4): distribute the -3 to the 2 x and -4 or multiply the -3 by 2 x and -4, -3(2 x) is -6 x and -3(-4) is 12 so the answer is -6 x + 12.

Distributive Property The distributive property means to multiply terms. Examples: a. Simplify 3 a(4 b – 2) : 3 a(4 b) = 12 ab and 3 a(-2) = -6 a so the answer is 12 ab – 6 a or 12 ab + - 6 a b. Simplify 3(2 x -3) + 5 : First, you multiply the 3 by 2 x and -3 and then after that is done you need to add 5 3(2 x) – 3(3) +5 = 6 x -9 + 5 = 6 x – 4 c. Simplify 3(2 x -3) +5(x + 2) : This problem has 2 sets of parentheses so you have to distribute twice. First you multiply 3 by 2 x and -3 and then multiply 5 by x and 2. Then you combine like terms. 3(2 x-3) = 6 x -9 and 5(x+2) = 5 x +10 , now you combine like terms with 6 x -9 + 5 x + 10 to get 11 x +1. d. Simplify -4(2+a) + 3(2 a -1) : First, you have to multiply the numbers outside the parentheses by the numbers inside. -4(2 + a) = -8 – 4 a and 3(2 a -1) = 6 a -3. Then combine like terms -8 -4 a +6 a -3 = 2 a -11 or 2 a + -11.

Writing expressions from descriptions We will write expressions, using numbers and variables, from a verbal description. You will have to know the terms sum, difference, product and quotient. Sum refers to addition, difference refers to subtraction, product refers to multiplication and quotient refers to division. There are other terms that will be used and will discuss those as we need. An example of a verbal description is: what is the sum of a number and 6 ? The expression would be x + 6 because sum refers to addition and “a number” means to use a variable. I chose x but you could use any letter to represent the number so another answer could be n + 6. Examples: a. The product of 8 and a number. Product is multiply so an answer is 8 n or 8(x). b. The quotient of a number and 2. Quotient means divide so an answer is n / 2. c. The quotient of a 2 and a number. Quotient means divide so an answer is 2 / x. The examples b and c are similar but when using division the order of the terms is important. When you divide the numbers 8 by 2 it is different than 2 by 8.

Writing expressions from descriptions Examples of writing expressions from verbal descriptions a. The difference of a number and 2. Difference is subtracting so n -2. b. The difference of 2 and a number. Difference is subtracting so 2 –n. These 2 examples are using subtraction and the order matters with subtraction. When you subtract 6 -2 it is different from 2 -6. c. A number doubled. This means multiplying by 2 so an answer is 2 x. d. A number tripled. This means multiplying by 3 so an answer is 3 n. e. Half of a number. This means dividing by 2 so an answer is n /2. f. Five greater than a number. This would be adding so an answer is 5 + n or n + 5. This is not using the greater than sign, > , because it doesn’t say “is greater than” but just says greater than. Also, if I said what is 5 greater than 10 you would add 5 and 10 to get 15.

Writing expressions from descriptions