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Math 009 Unit 5 Lesson 2

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Constants, Variables and Terms A variable is represented by a letterx is a variable A number is often called a constant-9 is a constant A term is a variable or a constant or the product of a constant and variables. x is a term 7 is a term 12x is a term -4x 3 is a term The terms of an expression are separated by addition signs or subtraction signs The expression x 2 – 3x + 5 has three terms

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Identifying the parts of a term 5x 3 x is the variable of the term 5 is the coefficient of the term 3 is the exponent of the variable What is the coefficient of the term: -17x 7 What is the exponent of the term: 23x 10

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Identifying like terms Two terms are called like terms if their variable parts are exactly the same – including any exponents. 5x and -3x x 2 and x 27 and -3 11x 2 and 5x 2 3x and 3 like terms not like terms

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Distributive Property If a, b, and c are real numbers, then a(b + c) = ab + ac The Distributive Property can also be written this way ab + ac = (b + c)a This second form helps in combining like terms 5x + 3x Simplify the following: = (5 + 3)x = 8x 5y 2 – 11 y 2 = (5 – 11)y 2 = - 6y 2 Can you simplify this process, so that you don’t have to write so much each time you do a problem? Terms cannot be combined by addition or subtraction unless they are like terms.

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The process of combining like terms can be summarized as add or subtract the coefficients of like terms as indicated the variable part remains unchanged Simplify each of the following: 2x + 3y – 7x + 10y -5x + 13y 8x – 15x + 7 -7x + 7 -3x 2 + 7 + 8x 2 – 14 + x – 5x 5x 2 – 4x – 7 2x – 7x + 3y + 10y 8x 2 – 3x 2 + x – 5x + 7 – 14

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Simplifying expressions by combining like terms Simplify each of the following 8x – 3 + 5x + 18= 8x + 5x – 3 + 18 = 13x + 15 9x + 5y – 3x – 2y= 9x – 3x + 5y – 2y = 6x + 3y 6u + 7v – 8 – 12v + 14 + 9u = 6u + 9u + 7v – 12v – 8 + 14 = 15u – 5v + 6

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Simplifying expressions by combining like terms Simplify each of the following 3x 2 – 2x + 5 – x 2 – 18= 3x 2 – x 2 – 2x + 5 – 18 = 2x 2 – 2x – 13 -7x 2 + 4xy + 8x 2 – 12xy= -7x 2 + 8x 2 + 4xy – 12xy = x 2 – 8xy 7x 2 y – 15xy 2 + 3 + 12xy 2 – 8x 2 y = 7x 2 y – 8x 2 y – 15xy 2 + 12xy 2 + 3 = -x 2 y – 3xy 2 + 3

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Simplifying expressions involving the Distributive Property Remember that multiplications are done before additions or subtractions 7(2x – 5) + 3(4x – 3)=14x – 35+ 12x – 9 = 14x + 12x – 35 – 9 = 26x – 44 6y + 2(2y + 3)=6y+ 4y + 6 = 10y + 6

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Simplifying expressions involving the Distributive Property Remember that multiplications are done before additions or subtractions 2c – 3(c + 4) – 2(2c – 3)=2c– 3c – 12 = 2c – 3c – 4c – 12 + 6 = - 5c – 6 -3(2a – 5) – 2(4a + 3)=-6a + 15– 8a – 6 = -14a + 9 = -6a – 8a + 15 – 6 – 4c + 6

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