Math 017 Materials With Exercises

) This should be written as 4x 2 (3x 2)Notice that “subtract from”causes us to reverse the order of the expressions. Removing parentheses following aminus sign reverses signs of all terms inside parentheses ( 3 x „becomes‟ 3x, 2„becomes‟ 2 ). After removing parentheses we collect like terms ( x's separately,numbers separately) to get 4x 2 (3x 2) 4x 2 3x 2 7x 4c) This should be written as ( 3x 2)( 4x 2). To remove parentheses we applythe Distributive Law ( 3x 2)( 4x 2) 3x(4x) 3x(2) 2( 4x) 2(2)12x2 6x 8x 4 12x214x 455Example 6.5 Rewrite the expression 3( x 2) (4 x ) in its equivalent form without parenthesesand simplify by collecting like terms.Solution:3( x5 2) (4 x5) 3x5 (3)( 2) 4 x5 3x5 x5 6 4 4x510The square of the sum or the difference of two expressionsThe Distributive Law, together with the ability to collect like terms, allows us to derive two importantformulas.2Consider ( a b) . Our goal is to write the expression in its equivalent form without parentheses.Thus the following is true.( a b)2 use the definition of the square of the expression( a b)(a b)apply the Distributive Law for the product of two sums22a ab ba b collect like terms22a 2ab bThe Square of the Sumof Two Expressions.2 22( a b) a 2ab bNotice that this means that the square of the sum of two terms is not equal to the sum of their2 2 2squares. In other words ( a b) a b .Using exactly the same technique, one can prove thatThe Square of the Differenceof Two Expressions.2 22( a b) a 2ab bAgain, this means that the square of the difference of two terms is not equal to the difference of2 2 2their squares. In other words ( a b) a b .64