CPM Homework Help : CCA Problem 3-81

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3-81.

Find each of the following products by drawing and labeling a generic rectangle or by using the Distributive Property.

$−4y(5x+8y)$

Step 1(a):
Make and label a generic rectangle.
Generic rectangle left edge $-4y$
interior left blank
interior right blank
bottom edge left $5x$
bottom edge right $+8y$
Step 2(a):
Fill in the boxes, and then add the boxes' labels together
Generic rectangle left edge $-4y$
interior left $-20xy$
interior right $-32y^2$
bottom edge left $5x$
bottom edge right $+8y$
Answer (a):
$−20xy−32y^2$

$9x(−4+10y)$

Step 1(b):
Distribute the $9x$ over each of the terms in the parentheses.
$9x(−4)+9x(10y)$
Step 2(b):
Simplify.
Answer (b):
$−36x+90xy=90xy−36x$

$(x^2−2)(x^2+3x+5)$

Hint (c):
Try using a generic rectangle to solve this problem.
Answer (c):
$x^4+3x^3+3x^2−6x−10$

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