### Home > INT1 > Chapter 6 > Lesson 6.1.1 > Problem6-8

6-8.

Copy and complete the area models below. Then write the area of each rectangle as a product equivalent to a sum.

1.  Generic rectangle left edge$6$ interior left blank interior right blank bottom edge left$13x$ bottom edge right$-21$

To write the area as a sum:
Find the area of each of the rectangle's sections. Then, add them together.

To write the area as a product:
Multiply the total length by the total width, but don't simplify it.

As a sum: $78x−126$
As a product: $6(13x−21)$

1.  Generic rectangle left edge top$x$ interior left top blank interior right top blank left edge bottom$-5$ interior left bottom blank interior right bottom blank bottom edge left$x$ bottom edge right$+3$

See the help for part (a).

As a sum: $x^2−2x−15$
As a product: $(x−5)(x+3)$

1.  interior left$16x^2$ interior middle$-24x$ interior right$4$

Find the greatest common factor of the areas. That will be the width. Then divide each area by the width to find the length. Then follow the steps for part (a).

 Generic rectangle left  edge$\mathbf{4}$ interior left $16x^2$ interior right$-24x$ interior right $4$ bottom edge left$\mathbf{4x^2}$ bottom edge middle$\mathbf{-6x}$ bottom edge right$\mathbf{1}$
1.  Generic rectangle left top edge$3x$ interior top left blank interior top right blank left bottom edge$-2$ interior bottom left blank interior bottom left blank bottom left edge$x$ bottom right edge$+4$

See the help for part (b).