Math 017 Materials With Exercises

Example 5.5 Factor22 2 4 3 3xy from the expression 4xy xy 3xy .Solution:4x2y2 xy43 3xy3224xy xy2 xy2xyxy4233xy2xy3 xy2(4x y2 3x2y)Example 5.6 Factor ( a 2b)from the expression 4x(a 2b) ( a 2b).Solution: 4x(a 2b)a 2b4x( a 2b) ( a 2b) ( a 2b) ( a 2b)(4x1) ( a 2b)a 2ba 2bPlease, notice that 1 and thus 1 appears as one of the terms inside parentheses.a 2bExample 5.7 Factor 41 from the expression1 3 x y .4 4Solution:1 3 1x y 4 4 4 1x4143y4141 1 4 441 x 3441 1 y ( x 3y) 4Example 5.8 Factor 5 from the expression x 5.Solution: x 5 x x 5 5 51 5 5 5 Factorization of −1Consider a b . We can factor 1 a b a b ( 1) ( 1)(a b) (a b) (b a) 11Factorization of 1 causes the signs in front of each term in the original expression to change (in ourexample a changes to a , b changes to b ). Thus, a b ( b a)as we see above.Example 5.9 Factor 1 from the expression2 x y z .Solution:2x y z 1(2x y z) (2x y z)53