CPM Homework Help : INT2 Problem 3-44

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3-44.

Use an area model to multiply each of the following expressions. Write each expression both as a sum and as a product.

$(2x+5)(x+6)$
Hint 1(a):
Draw a rectangular area model and label the length and width.
Show (a):
$2x$
$+5$
$x$
$+6$
Hint 2(a):
Fill in the area model by multiplying the length and width of each box.
$2x$
$+5$
$x$
$2x^2$
$5x$
$+6$
$12x$
$30$
Answer (a):
Write an equation showing the product is the sum of the parts.
Area as a sum: $2x^{2} + 12x + 5x + 30$ or $2x^{2} + 17x + 30$
Area as a product: $\left(2x + 5\right)\left(x + 6\right)$

$(m-3)(3m+5)$
Hint (b):
See the help for part (a).
Answer (b):
$m$
$-3$
$3m$
$3m^2$
$-9m$
$+5$
$5m$
$-15$
Area as product: $\left(m − 3\right)\left(3m + 5\right)$
Area as sum: $3m^{2} − 4m − 15$

$(12x+1)(x^2-5)$
Hint (c):
See the help for part (a).
Partial Answer (c):
$12x$
$+1$
$x^2$
$12x^3$
$x^2$
$-5$
$-60x$
$-5$

$(3-5y)(2+y)$
Hint (d):
See the help for part (a).

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