a Make a generic rectangle where one factor is in the top row and the other factor is written vertically in the left-side column.
B
b Make a generic rectangle where one factor is in the top row and the other factor is written vertically in the left-side column.
C
c Make a generic rectangle where one factor is in the top row and the other factor is written vertically in the left-side column.
D
d Make a generic rectangle where one factor is in the top row and the other factor is written vertically in the left-side column.
A
a (2x+5)(x+6)=2x^2+17x+30
B
b (m-3)(3m+5)=3m^2-4m-15
C
c (12x+1)(x^2-5)=12x^3+x^2-60x-5
D
d (3-5y)(2+y)=-5y^2-7y+6
Practice makes perfect
a Let's build a generic rectangle where the factor 2x+5 is in the top row and the factor x+6 is written vertically in the left-side column.
2x
5
x
2x^2
5x
6
12x
30
We get ( 2x+5)( x+6)=2x^2+5x+12x+30=2x^2+17x+30.
b As in part A, we build a generic rectangle where the factor m-3 is in the top row and the factor 3m+5 is written vertically in the left-side column.
m
-3
3m
3m^2
-9m
5
5m
-15
That way, we get ( m-3)( 3m+5)=3m^2-9m+5m-15=3m^2-4m-15.
c As before, we write a generic rectangle where the factor 12x+1 is in the top row and the factor x^2-5 is written vertically in the left-side column.
12x
1
x^2
12x^3
x^2
-5
-60x
-5
Hence, ( 12x+1)( x^2-5)=12x^3+x^2-60x-5.
d Finally, we write down the last generic rectangle where the factor 3-5y is in the top row and the factor 2+y is written vertically in the left-side column.
