Page 114 - Algebra 1

Example
2
Combining Like Terms With Exponents
Simplify each expression.
a. x5 +y3 +x5 +y3 SOLUTION
x5 +y3 +x5 +y3
=x5 +x5 +y3 +y3
= (1 + 1)x5 + (1 + 1)y3 = 2x5 + 2y3
b. 3k2 –2k2 +4k2 +2kx4 +kx4 SOLUTION
3k2 –2k2 +4k2 +2kx4 +kx4 = (3 – 2 + 4)k2 + (2 + 1) kx4 =5k2 +3kx4
c. 2x2y3 + xy - 8y3x2 – 5yx SOLUTION
2x2y3 + xy - 8y3x2 – 5yx =2x2y3 -8y3x2 +xy–5xy =2x2y3 -8x2y3 +xy–5xy = (2 - 8)x2y3 + (1 -5)xy = -6x2y3 -4xy
Rearrange the terms.
Use the Distributive Property. Simplify.
Use the Distributive Property. Simplify.
Rearrange the terms. Rearrange the factors.
Use the Distributive Property. Simplify.
Hint
The coefficient of x is 1.
The coefficient of -x is -1.
Reading Math
It is customary to write the factors of a term in alphabetical order. So, x2zy3 is written x2y3z.
Example
3
Application: Measurement
Olympic competition offers three equestrian disciplines: dressage, show jumping, and endurance. The diagram represents the measurements for a regulation dressage arena.
3x + 3
Find the perimeter of the arena as a simplified variable expression. Then evaluate the expression for x = 19.5 meters.
SOLUTION
P = 2l + 2w
P = 2(3x + 3) + 2(x - 1) P=6x+6+2x-2
P = 8x + 4
P = 8(19.5) + 4
Write the formula for the perimeter of a rectangle.
Substitute for l and w.
Use the Distributive Property. Combine like terms. Substitute 19.5 for x. Multiply. Then add.
x - 1
Online Connection www.SaxonMathResources.com
P = 156 + 4 = 160
The perimeter of the dressage arena is 8x + 4 or 160 meters.
Lesson 18 99