CPM Homework Help : INT1 Problem 6-8

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6-8.

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

Generic rectangle left edge $6$
interior left blank
interior right blank
bottom edge left $13x$
bottom edge right $-21$
Hint (a):
To write the area as a sum:
Find the area of each of the rectangle's sections. Then, add them together.
More Help (a):
To write the area as a product:
Multiply the total length by the total width, but don't simplify it.
Answer (a):
As a sum: $78x−126$
As a product: $6(13x−21)$

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 $+3$
Hint (b):
See the help for part (a).
Answer (b):
As a sum: $x^2−2x−15$
As a product: $(x−5)(x+3)$

interior left $16x^2$
interior middle $-24x$
interior right $4$
Hint (c):
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).
More Help (c):
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 $\mathbf{1}$

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 $+4$

Hint (d):

See the help for part (b).

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