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Review Day! copyright©amberpasillas2010 a(b c) a b a c or a(b c) a b a c copyright©amberpasillas2010 I am going to show you 2 ways to solve this expression. 3(4 5) Order of Operations 3(4 5) 3(9) 27 Distributive Property 3(4 5) 3(4) 3(5) 12 15 27 Let’s see if it works the same way for subtraction! copyright©amberpasillas2010 I am going to show you 2 ways to solve this expression. 5(10 3) Order of Operations 5(10 3) 5(7) 35 Distributive Property copyright©amberpasillas2010 5(10 3) 5(10) 5(3) 50 15 35 So you are probably thinking why use the Distributive Property when Order of Operations is easier? Just watch! Order of Operations 4(x 2) Distributive Property You can’t add x + 2 because they are different terms! 4(x 2) 4(x) 4(2) 4x 8 Why use the Distributive Property? It helps you simplify when letters are used! copyright©amberpasillas2010 The Distributive Property helps with mental math! 4 • 83 4(80 + 3) 80 + 3 4 4(80) + 4(3) = 320 + 12 = 332 x + 4 5(x + 4) 5 5(x)+ 5(4) = 5x + 20 copyright©amberpasillas2010 Use the distributive property to simplify. 1) 2(x + 8) 2) 3(a - 8) 2x + 16 3a - 24 3) -7(8 - m) 4) 4(5- a) -56 + 7m 20 - 4a 5) (10 - k)5 6) x(y + z) xy + xz 50 - 5k Identity Property of Addition a0a Identity remains the same Zero is called the additive identity Identity Property of Multiplication a 1 a Identity remains the same One is called the multiplicative identity copyright©amberpasillas2010 Name the property shown below. 1) (6 + 3) + 1 = (3 + 6) + 1 Commutative Property of Addition Order doesn’t matter Flip-Flop 2) 10 (8 3) (10 8) 3 Associative Property of Multiplication Re-Grouping copyright©amberpasillas2010 Terms: Numbers and/or variables tied together by multiplication or division but separated by addition or subtraction. How many terms? 6 terms 6x 7x 3y 4abc 2 k 2 m copyright©amberpasillas2010 Coefficient: The number preceding the variable in a variable term. How many coefficients? 5 coefficients 6x 7x 3y 4abc 2 1k 2 m The number IN FRONT OF THE VARIABLE copyright©amberpasillas2010 Constant: The numerical terms. (NUMBERS ONLY) How many constants? 1 constant 6x 7x 3y 4abc 2 1k 2 m The numbers WITH NO VARIABLES! copyright©amberpasillas2010 You can use what you have learned about properties when combining like terms. copyright©amberpasillas2010 Simplify each expression by using the Distributive Property and combining like terms. 1) 7(x + 4) + 2x 7x + 28 + 2x 2) 5x + 3(x + 1) 5x + 3x + 3 8x + 3 9x + 28 copyright©amberpasillas2010 Simplify each expression by using the Distributive Property and combining like terms. 3) a + 2(4 + a ) - 1 a + 8 + 2a - 1 4) 3(b - 2) + 6b 3b - 6 + 6b 3a + 7 9b - 6 copyright©amberpasillas2010 Take Out Your Study Guide!!! copyright©amberpasillas2010 #7 Coefficient: The number in front of the variable. 5 Coefficients Ex: 3x -2y 1 m 7x y 2 2 2 m 3 Terms: The numbers and variables separated by addition & subtraction. Ex: 3x + 2y – 8 3 Terms Constant: The numerical terms. Ex: 5x + 9 – 6 2 Constants copyright©amberpasillas2010 Like Terms and Unlike Terms #8 Terms in an expression are like terms if they have identical variable parts. Like Terms 3 5 8 10x -2x 8x 2 1 x 8x 9x 2 2 copyright©amberpasillas2010 Unlike Terms 3 x 10x -2x 2 3 x 8x 2