Warm up – Find the GCF
54a 2b
63a 2b2c
54a 2b 
63a 2b2c 
180ab3c2 
9ab
180ab3c 2
10-2 Factoring using the
Distributive Property
Objective: To use the GCF and
the distributive property to factor.
Standard 11.0
FACTOR: WORK BACKWARDS!
Question
Answer: GCF (÷ out)
1)
3x + 3
1)
3(x + 1)
2)
2x2 – 6x
2)
2x(x – 3)
3)
2ab – 9a
3)
a(2b – 9)
EXAMPLE 1
9x2y + 6xy2
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GCF: 3xy
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Divide it to the outside of some parenthesis
Then write what you have left inside of the
parenthesis for each term
3xy( 3x + 2y )
 3xy(3x+2y)
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Quick TOO
12 x  18x
3
6x (2x  3)
2
2
28a b  56abc
2
2
20abc  15a c  5ac
2
28ab(a  2c )
2
5ac(4b  3a  1)
Grouping
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a(x + y) + b(x + y)
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What do they have in common?
(x + y)
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(x + y)( a + b )
(x+y)(a+b)
Example 2: Factoring by Grouping

3am – 6bm + 5an – 10bn

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(3am – 6bm) + (5an – 10bn)
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Group in pairs
Factor out GCF from each pair
3m(a – 2b) + 5n(a – 2b)
(a – 2b)( 3m + 5n )
Try with mathlete
1)
(hint: group!)
a2 + 3ab + 2ac + 6bc
(a + 3b)(a + 2c)
2) 15x – 3xy + 20 – 4y
(5 – y)(3x + 4)
How can we check our answers?
BOX method!
Example 3
2my + 7x + 7m + 2xy
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Reorder before grouping!
2my + 2xy + 7m + 7x
(2my + 2xy) + (7m + 7x)
2y(m + x) + 7(m + x)
(m + x)(2y + 7)
Example 4
6xy – 15x – 8y + 20
(6xy – 15x) + (-8y + 20)

Notice that I changed it to “+ (-8y)”, keep
negatives with their numbers!
3x(2y – 5) + 4(-2y + 5)

Factor a negative from 2nd parenthesis
3x(2y – 5) – 4(2y – 5)
(2y – 5)(3x – 4)
TOO
1) rx + 2ky + 2ry + kx
Hint: Reorder
2) 10mx + 5rx – 8m – 4r
Hint: Pay attention to your negatives
Homework
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Pg. 570 # 33-49 odd
Go to the choir show!!!!!!!!!!!!!!!!
Math Lab Warm up
3a b(6a  9b)
2
(3x  4)(3x  4)
( x  9)(2 x  1)
(3x  4)2
GCF


What does GCF stand for?
Greatest Common Factor
Example: Find the GCF
4xy and -6x
GCF: 2x
Find the GCF
26xy
4
16xy
3
8x
2
2x
Factoring with GCF
6x  3 y
15wx  35wx
24 x  12 y
2
2
2
11x  44 x y
2
Grouping

Use grouping when there are 4
terms.
3ax  6bx  8b  4a
TOO
a  2ab  a  2b
2
(a  1)(a  2b)
8ac  2ad  4ad  bd (2a  b)(4c  d )
Puzzle time

1 puzzle paper
1 colored paper
1 scissors

Listen for instructions…
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