Page 259 - Algebra 1

Example
2
Math Reasoning
Justify Why can the final expression not be simplified further?
__
Simplify m (axp - 2m p ).
SOLUTION
__
m(apx -2mp)
z mk
44
z mk
=mapx - m·2mp
__44
Distributing Over Subtraction
44
_m Distribute z.
Simplify.
Notethatz≠0,k≠0,andm≠0becauseanyof thosevalueswould make a denominator equal to zero. Although there is not an m in the denominator of the final expression, there is one in the denominator of the original expression; that is why m ≠ 0.
When simplifying an expression with negative exponents, the final expression should not have negative exponents.
Simplifying with Negative Exponents
Simplify each expression.
zmk z
_ _5 4
= apx - 2mp ;z≠0,k≠0,m≠0
zk z
Example
3
b3 (2b2 f-3d) ___
a.d-3 d-b SOLUTION
b3 (2b2 f-3d) ___
d-3 d-b
b3 ·2b2 b3 ·f-3d b3
___ = d-3 · d - d-3b Distribute d-3 .
Product Property of Exponents Simplify.
2b5 b3f -3d __
= d -2 - d -3b _2 4
=2b5d2 - bd ;d≠0,b≠0,f≠0 f3
__
b. n-1 mx +5n p
m (cn-3p-5
-4 -5 )
SOLU_TION
_-1 n
mx m (cn-3p-5
-4 -5
n-1x 5n-5p-5 __
= cn-3p-5 + m
n2xp5 5 __
+5n p
)
n-1mx n-1 · 5n-4p-5 n-1 ____
= mcn-3p-5 + m Distribute m .
Simplify. Simplify.
= c + mn5p5 ;c≠0,m≠0,n≠0,p≠0
244 Saxon Algebra 1