Transcript Difference of Squares - 2

Objective
The student will be able to:
factor using difference of squares.
SOL: A.2c
Designed by Skip Tyler, Varina High School
Factoring Chart
This chart will help you to determine
which method of factoring to use.
Type
Number of Terms
1. GCF
2. Difference of Squares
2 or more
2
Determine the pattern
1
4
9
16
25
36
…
= 12
= 22
= 32
= 42
= 52
= 62
These are perfect squares!
You should be able to list
the first 15 perfect
squares in 30 seconds…
Perfect squares
1, 4, 9, 16, 25, 36, 49, 64, 81,
100, 121, 144, 169, 196, 225
Review: Multiply (x – 2)(x + 2)
First terms: x2
Outer terms: +2x
Inner terms: -2x
Last terms: -4
Combine like terms.
x2 – 4
Notice the
middle terms
eliminate
each other!
x
-2
x2
-2x
+2 +2x
-4
x
This is called the difference of squares.
Difference of Squares
2
2
a - b = (a - b)(a + b)
or
2
2
a - b = (a + b)(a - b)
The order does not matter!!
4 Steps for factoring
Difference of Squares
1. Are there only 2 terms?
2. Is the first term a perfect square?
3. Is the last term a perfect square?
4. Is there subtraction (difference) in the
problem?
If all of these are true, you can factor
using this method!!!
1. Factor x2 - 25
When factoring, use your factoring table.
Do you have a GCF? No
Are the Difference of Squares steps true?
x2 – 25
Two terms? Yes
1st term a perfect square? Yes
2nd term a perfect square? Yes
Subtraction? Yes
( x + 5 )(x - 5 )
Write your answer!
2. Factor 16x2 - 9
When factoring, use your factoring table.
Do you have a GCF? No
Are the Difference of Squares steps true?
16x2 – 9
Two terms? Yes
1st term a perfect square? Yes
2nd term a perfect square? Yes
Subtraction? Yes
(4x + 3 )(4x - 3 )
Write your answer!
3. Factor 81a2 – 49b2
When factoring, use your factoring table.
Do you have a GCF? No
Are the Difference of Squares steps true?
81a2 – 49b2
Two terms? Yes
1st term a perfect square? Yes
2nd term a perfect square? Yes
Subtraction? Yes
(9a + 7b)(9a - 7b)
Write your answer!
Factor
1.
2.
3.
4.
2
x
(x + y)(x + y)
(x – y)(x + y)
(x + y)(x – y)
(x – y)(x – y)
Remember, the order doesn’t matter!
–
2
y
4. Factor
2
75x
– 12
When factoring, use your factoring table.
Do you have a GCF? Yes! GCF = 3
3(25x2 – 4)
Are the Difference of Squares steps true?
Two terms? Yes
3(25x2 – 4)
1st term a perfect square? Yes
2nd term a perfect square? Yes
Subtraction? Yes
3(5x + 2 )(5x - 2 )
Write your answer!
Factor
1.
2.
3.
4.
2
18c
prime
2(9c2 + 4d2)
2(3c – 2d)(3c + 2d)
2(3c + 2d)(3c + 2d)
You cannot factor using
difference of squares
because there is no
subtraction!
+
2
8d
Factor -64 +
1.
2.
3.
4.
prime
(2m – 8)(2m + 8)
4(-16 + m2)
4(m – 4)(m + 4)
Rewrite the problem as
4m2 – 64 so the
subtraction is in the
middle!
2
4m