2.05 Factoring Difference of Squares
Perfect Square Trinomials
Basic
Algebra: One Step at a Time. Pages
157-163: 67, 72, 74, 75
Dr. Robert J. Rapalje
Seminole Community College
Sanford, FL 32773
To see
Section 2.05, with
detailed explanations, examples, exercises, and answers,
click here!
p. 162: 67.
Notice that
and 
are both perfect
squares.
The First
times
First
must be
: 
times
The
Last times
Last
must be 16:
4 times
4.
Because the 16 is negative, use opposite signs.
The factor
is itself a difference of squares, and so it must be
re-factored. However, the factor
is the SUM of squares. It does not re-factor, and it must
be left as it is in the final answer.
Final Answer!!
p. 162: 72.
Notice that
and 
are both perfect
squares.
The First
times
First
must be
:
times
The
Last times
Last must be 81:
9
times 9.
Because the 16 is negative, use opposite signs.
The factor
is itself a difference of squares, and so it must be
re-factored. However, the factor
is the SUM of squares. It does not re-factor, and it must
be left as it is in the final answer.
Final Answer!!
p. 163:
74.
Notice that
First times
First
must be
: times
The
Last times
Last must be
and the
OI
term must add up to
13x2
(Try 9
• 4, both positive)
O term
is 4x2,
and the I
term is
9x2,
for a total of 13x2 ,
The factors
and 
are both sums of squares! They cannot be NOT re-factored
so this is the final answer.
p.
162: 75.
Notice that
First times
First
must be
: times
The Last
times Last
must be
and the
OI
term must add up to
13x2 (Try 9
• 4, both negative)
O term
is −4x2,
and the I term
is
−9x2,
for a total of
−13x2
The factors
and 
are both difference of squares. Each must be re-factored
so this is NOT the final answer.
Final Answer!!
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