Distributive Property Using Area
NAME ___________________________
Write the expression that represents the area of each rectangle.
1.
5
2.
7
3.
4
a
4.
3
x
x
m
Find the area of each box in the pair.
x
5.
3
6.
a
9
7.
4
x
2
x
7
Write the expression that represents the total length of each segment.
x
8.
9
9.
______________
x
4
10.
______________
a
2
______________
Write the area of each rectangle as the product of length  width and also as a sum of the areas of
each box.
11.
x
7
12.
x
12
13.
a
8
5
x
AREA AS
PRODUCT
AREA AS
SUM
5(X+7)
5X+35
a
AREA AS
PRODUCT
AREA AS
SUM
AREA AS
PRODUCT
AREA AS
SUM
This process of writing these products as a sum uses the distributive property.
Use the distributive property to re-write each expression as a sum. You may want to draw a rectangle
on a separate page to follow the technique above.
14.
16.
18.
20.
4( x  7) =_____________
2( x  4) =____________
a (a  1) =___________
4(a  4) =___________
15.
17.
19.
21.
7( x  3) =___________
x( x  9) =___________
3m(m  2) =___________
a(a  12) =__________
© 2007 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Factoring a Common Factor
Using Area
NAME ___________________________
Fill in the missing information for each: dimensions, area as product, and area as sum
1.
2.
x
3.
4.
6
2
8
5 5x
20
6x
x
48
10x
30
___2(x+6)____
___________
___________
___________
___2x+12____
___________
___________
___________
Fill in the missing dimensions from the expression given.
5. 5 x  35  5(______)
6. 2 x  12  2(______)
8. 7 x  21  __(______)
9. 3 x  15  3(______)
7. 3 x  21  __(______)
10. 5 x  45  ________
This process of writing a sum or difference as the product of factors is called factoring.
Factor these:
11. 4 x  16  _____________
12. 7 x  35  ______________
13. 9 x  81  _____________
14. 4 x  18  __________
© 2007 National Council of Teachers of Mathematics
http://illuminations.nctm.org
More Factor Using Area
NAME __________________________
Fill in the missing information for each: dimensions, area as product, and area as sum
1.
2.
x
3.
4.
-7
3
-5 -5x
x2
20
10
a
10x
a2
-3a
___3(x-7)____
___________
___________
___________
___3x-21____
___________
___________
___________
Fill in the missing dimensions from the expression given.
5. x 2  3 x  x(______)
8. 4 x  10  ________
6. x 2  5 x  x(______)
9. a 2  5a  _________
7. 6 x  21  3(______)
10. m 2  m  ________
When factoring expression, you have to consider that the common factor may be a
variable instead of (or addition to) a number.
Factor these:
11. t 2  6t  _____________
12. 10 x  35  ______________
13. 6 x  21  __________
14. 9a 2  15a  _____________
© 2007 National Council of Teachers of Mathematics
http://illuminations.nctm.org
Greatest Common Factor
NAME __________________________
Complete the factorization for each:
1.
a. 3 x 2  15 x  3(_______)
b. 3 x 2  15 x  x(_______)
c. 3 x 2  15 x  3 x(_______)
2. Which of the above factorizations for 3 x 2  15 x do you think is the ‘best’? Why?
_____________________________________________________________________
3.
a. 4a 2  12a  4(_______)
b. 4a 2  12a  a(_______)
c. 4a 2  12a  4a(_______)
4. Which of the above factorizations for 4a 2  12a do you think is the best? Why?
_____________________________________________________________________
In each case the third factorization is the best because you’ve factored out the greatest
common factor (GCF).
Factor each expression below. Be sure to find and use the greatest common factor.
5. 5 x 2  15 x  __________
6. 3 x 2  12 x  __________
7. 6 x  4  __________
8. 7 x 2  9 x  __________
9. 5 x 2  5 x  __________
10. 9a 2  12a  __________
© 2007 National Council of Teachers of Mathematics
http://illuminations.nctm.org