Math 009 Unit 5 Lesson 2

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

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

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

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.

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 x x x 2 – 14 + x – 5x 5x 2 – 4x – 7 2x – 7x + 3y + 10y 8x 2 – 3x 2 + x – 5x + 7 – 14

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

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 xy 2 – 8x 2 y = 7x 2 y – 8x 2 y – 15xy xy = -x 2 y – 3xy 2 + 3

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

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 – = - 5c – 6 -3(2a – 5) – 2(4a + 3)=-6a + 15– 8a – 6 = -14a + 9 = -6a – 8a + 15 – 6 – 4c + 6