Page 260 - Algebra 1

Example
4
Distributing Over Multiple Operations
Simplify each expression.
___ a. ab axb + 2bx - 4 (c2
) ab axb + 2bx - 4
c2 c SOLUTION
___ (c2
)
c2__c _ _ = ab·axb + ab·2bx - ab·4 Distribute ab.
c2 · c c2 c2 · c2 = a2b2x + 2ab2x - 4ab; c ≠ 0
c2 Simplify.
= =
d - d2 + d-1 Distribute d2 .
___ c3 c2 c4
___
b. g2h(g-2xh-2h4x-1+ 9)
d2 d-1 d-3 SOLUTION
g2h(g-2xh-2h4x-1+ 9) ___
Hint
When a variable has no exponent, it is implied that the exponent is 1.
Any variable or number raised to the 0 power equals 1.
d2 d-1
d-3
g0xh2 2h5x-1g2 9g2h g2h ___ _
xh2 2h5g 2 __
2
d - xd 2 + 9dg
Application: Furniture
h; d ≠ 0 and x ≠ 0
Simplify.
Example
5
_
A tabletop that is in the shape of a trapezoid has height a2c , and bases
Hint
The formula for the area of a trapezoid is
A=_1h(b1 +b2). 2
_3_ b
b and da . The area of the tabletop is represented by the expression c c2
a2c (b3 da ___
)
. Simplify the expression.
Distribute.
Multiply.
Simplify.
The area of the tabletop can be represented by the simplified expression
2b c + c 2
SOLUTION
a2c (b3 da ___
) a2cb3 a2c · da
2b c + c 2
__ = 2bc + 2bc2
= a2b3c + a3cd __
2bc 2bc2 a2b2 a3d
__ = 2 + 2bc
a2b2 a3d __
2 +2bc.
Lesson 39 245