CPM Homework Help : CCAA8 Problem 4-113

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

$( x + 5 ) ( x + 4 )$
Hint (a):
Create a generic rectangle. A generic rectangle: A rectangle with 4 quadrants. Values within the rectangle indicate area. Values on the outside edge represent length and width of the rectangle.
Hint 2 (a):
Put the products on the outside of the rectangle. A generic rectangle where the outside upper left edge is + 5 and the lower left edge is X. The bottom left edge is X and the bottom right edge is + 4.
Hint 3 (a):
Find the area of the smaller rectangles. The same rectangle in hint 2 with the interior labeled as follows: Upper left box is 5 X. Upper right box is 20. Lower left box is X squared. Lower right box is 4 X.
Hint 4 (a):
Write the areas as a sum.
$x^2+5x+4x+20$ .
Answer (a):
$(x+5)(x+4)=x^2+9x+20$

A generic rectangle: A rectangle with 4 quadrants. Values within the rectangle indicate area. Values on the outside edge represent length and width of the rectangle.

A generic rectangle where the outside upper left edge is + 5 and the lower left edge is X. The bottom left edge is X and the bottom right edge is + 4.

The same rectangle in hint 2 with the interior labeled as follows: Upper left box is 5 X. Upper right box is 20. Lower left box is X squared. Lower right box is 4 X.

$2y(y+3)$
Hint (b):
Follow the steps in part (a).