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Simplifying Expressions Objectives: …to simplify an expression by performing the distributive property …to simplify an expression by combining like terms Assessment Anchor: Not Available At This Time Vocabulary alert!! DISTRIBUTIVE PROPERTY – a way to simplify an expression that is multiplying a single term by a group of terms NOTES and EXAMPLES The distributive property is a very important property in mathematics, which allows us to simplify expressions in the following manner: ***For any numbers a, b and c… a(b + c) = ab + ac Look at the following examples that show the distributive property being applied: Ex. #1: 3(5 + 4) = 3(5) + 3(4) 3(9) = 15 + 12 27 = 27 Ex. #2: 8(2 + 6) = 8(2) + 8(6) 8(8) = 16 + 48 64 = 64 Ex. #3: 5 • 4 + 5 • 9 = 5(4 + 9) 20 + 45 = 5(13) 65 = 65 Ex. #4: 7 • 3 + 7 • 8 = 7(3 + 8) 21 + 56 = 7(11) 77 = 77 “Notice that whether the property is applied either forward or backward... the distributive property maintains the value of the expression.” Simplifying Expressions “Take what’s outside the parenthesis, and multiply it by each of the things inside the parenthesis.” Ex. #5: 5(x + 3) = 5(x) + 5(3) = 5x + 15 Ex. #6: 2(3x – 4) = 2(3x) – 2(4) = 6x – 8 7) 4(x + 6) = 9) 6(3x – 4) = 8) -2(x + 3) = 10) -8(2k + 1) = -------------------------------------------------------------------------------------------------11) -2(2x – 7) = 13) -3(9 – 2y) = 12) -7(5x – 2) = 14) -4(-3 – 5k) = Vocabulary alert!! TERM – a number, a variable, or product of a number and a variable(s) CONSTANT – a term with no variable part (i.e. a number) COEFFICIENT – a number that multiplies a variable LIKE TERMS – terms that have the same variable part Simplifying Expressions Combining like terms is another very important idea in mathematics, and is accomplished by adding the coefficients of the like terms. This is possible because of the distributive property. ***For any numbers a and b… Ex. #15: ax + bx = (a+b)x 4x + 7x = (4 + 7)x = 11x Ex. #16) 10y – 4y = (10 – 4)y = 6y Vocabulary familiarization activity 8x + 9 – 3 + 7y + 4x – 3y + 11 – xy Terms? Coefficients? Constants? Like terms? 17) 8y – 6y = 20) 10x + 5x = 18) 8x + 2y + 4x + 7y = 21) -3x + 10x + 4 – 18 = 19) 9 + 4x + 3y + 8y = 22) 4 – 12x + 4x – 10 = --------------------------------------------------------------------------------------------------23) 5 + x – 6y + x – 3y = 25) -4 – 2x – 9y + 3 – 7x + 2y = 24) -3xy + 4x – 9x + 4xy – 12x = 26) 8xy + 8x – 10 – 7y = --------------------------------------------------------------------------------------------------27) 2(x + 7) + 9x – 3 = 28) -3(2x + 9) + 2(5x + 1) =