Factoring Worksheet With Examples Page 30
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50Factoring Differences
8-5
of Squares
Main Ideas
A basketball player’s hang time is the length
•
Factor binomials
of time he or she is in the air after jumping.
that are the
Given the maximum height h a player can
differences
of squares.
jump, you can determine his or her hang time
2
•
Solve equations
t in seconds by solving 4 t
- h = 0. If h is a
involving the
perfect square, this equation can be solved
differences of
by factoring, using the pattern for the
squares.
difference of squares.
2
2
Factor
a
- b
A geometric model can be used to factor the difference
of squares.
ALGEBRA LAB
Difference of Squares
Use a straightedge to draw
Cut the small square from
Step 1
Step 2
two squares similar to those shown
the large square.
below. Choose any measures for a
and b.
a
b
b
b
b
a
b
b
a
a
b
b
a
a
Notice that the area of the large
The area of the remaining irregular
2
2
2
square is a
, and the area of the
region is a
- b
.
2
Look Back
small square is b
.
To review the
Cut the irregular region into
Rearrange the two pieces
Step 3
Step 4
product of a sum
and a difference,
two congruent pieces as shown
to form a rectangle with length
see Lesson 7-7.
below.
a + b and width a - b.
a
b
a
b
a
b
b
Region 1
a
b
a
b
a
b
a
b
Region 2
Region 2
b
a
a
A
R
NALYZE THE
ESULTS
1.
Write an expression representing the area of the rectangle.
Animation
2
2.
2
Explain why a
- b
= (a + b)(a - b).
447
Lesson 8-5 Factoring Differences of Squares
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