CPM Homework Help : INT1 Problem 3-101

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3-101.

Write an equation for each situation below showing that the area as a product is equal to the area as a sum.

$12x$
$+1$
$x$
$-5$

Hint (a):
Review the Math Notes box in Lesson 3.2.2.
Answer (a):
$(12x+1)(x−5)=12x^2−59x−5$

$2m^2$
$-4m$
$-1$
$3m$
$+5$

Hint (b):
See part (a).

$(2x+5)(x+6)$

Hint 1 (c):
Draw a generic rectangle and label the length and width.
Show (c):
$(2x + 5)(x + 6) = 2x^2 + 17x + 30$
$\color{red}{2x}$
$\color{red}{+5}$
$\color{red}{x}$
$\color{red}{+6}$
$\color{red}{2x}$
$\color{red}{+5}$
$\color{red}{x}$
$\color{red}{2x^2}$
$\color{red}{5x}$
$\color{red}{+6}$
$\color{red}{12x}$
$\color{red}{30}$
Hint 2 (c):
Fill in the grid by multiplying the length and width of each box.
Answer (c):
Write an equation showing the product is the sum of the parts.
Area as a sum $= 2x^2 + 12x + 5x + 30 = 2x^2 + 17x + 30$
Area as a product = $(2x + 5)(x + 6)$ .

$( 3 - 5 y ) ( 2 + y )$

Hint (d):
See the help for part (c).

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