Math 017 Materials With Exercises

Simplification of expressions with two or more terms by collecting like termsLet us examine the following expression 3x 4y 2x 6y. There are two “groups” of like terms inthis expression, x' s and y‟s. By changing the order of terms, we can group all like terms together,collect them, and as a result obtain a simplified expression.3x 4y 2x 6y 3x 2x 4y 6y (3 2) x (4 6) y 5x 2yExample 6.3 Simplify by collecting like terms.a) 3 x a 4x ab) 7y 5 12y y 6Solution:a) 3 x a 4x a 3x 4x a a (3 4)x a a xb) 7y 5 12y y 6 7y12y y 5 6 (7 121)y 1 4y1Simplification of expressions requiring the removal of parenthesesCollecting like terms often has to be preceded by removing parentheses. This is always done accordingto the Distributive Law.4m ( 2 m) 4m 2 m 4m m 2 5m 2 Parentheses following a plus sign areredundant, and thus can be dropped. Eachterm inside parentheses stays the same.3x (5x1) 3x 5x1 2x1Parentheses following a minus sign areremoved by reversing the sign of each terminside parentheses (operation equivalent tomultiplication by 1).a 3(a 2) a 3a 3( 2) a 3a 6 4a 6 We multiply 3 by each term in parentheses,and then collect all like terms.Example 6.4 Write each of the following expressions using algebraic symbols, then rewrite it in itsequivalent form without parentheses and, if possible, collect like terms.a) add 3x 2 and 4x 2b) subtract 3x 2 from 4x 2c) multiply 3x 2 and 4x 2Solution:a) This should be written as 3x 2 ( 4x 2). We remove parentheses (usingthe Distributive Law) and collect like terms ( x's separately, numbers separately) to get3x 2 ( 4x 2) 3x 2 4x 2 x63