Algebra Demystified 2nd Ed

Chapter 6 FaCtoring and the distributive ProPerty 139

6. 14x + 8 − (2x − 4) = 14x + 8 − 2x + 4 = 14x − 2x + 8 + 4
   = (14 − 2)x + 12 = 12x + 12


7. 16x−^4 + 3x−2 − 4x + 9x−4 − x−2 + 5x − 6
   = 16x−4 + 9x−4 + 3x−2 − x−2 − 4x + 5x − 6
   = (16 + 9)x−4 + (3 − 1)x−2 + (−4 + 5)x − 6
   = 25x−4 + 2x−2 + x − 6


8. 5713 74
   571

xy xy xy xy

xy xy

+  +  –  –  + 

+  +  –

()

= + 

+  +  + 

– 

374

537714

53

xy xy

xy xy xy xy

(  )

−

=− −

= xxy xy

xy xy

 ( ) 

+  – 

+  – 

77 3

2143

+

=

9. x^2 y + xy^2 + 6x + 4 − (4x^2 y + 3xy^2 − 2x + 5)
   = x^2 y + xy^2 + 6x + 4 − 4x^2 y − 3xy^2 + 2x − 5
   = x^2 y − 4x^2 y + xy^2 − 3xy^2 + 6x + 2x + 4 − 5
   = (1 − 4)x^2 y + (1 − 3)xy^2 + (6 + 2)x − 1
   = −3x^2 y − 2xy^2 + 8x − 1

Adding/Subtracting Fractions

With the distributive property and our ability to combine like terms, we can

simplify the sum and difference of fractions. Remember that the denominators

must be the same before we add or subtract fractions. Once we have the frac-

tions written with the LCD, we add or subtract their numerators. This involves

combining terms.

We generally leave the denominators factored.

EXAMPLES

Find the sum or difference.

2

41

2

4

1

11

4

4

21 4

x

x

xx

x

x

x

x

x

x

xxx

−

+

+

=

−

⋅ +

+

+

+

⋅ −

−

= ()++ −()

(()xx() ()()()(

xxx

xx

xx

+− xx

= ++ −

+−

= −+

14 +

22 4

14

(^2222)
1 −−4)
EXAMPLES
Find the sum or difference.