### Home > INT2 > Chapter 3 > Lesson 3.1.4 > Problem3-44

3-44.

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

1. $(2x+5)(x+6)$

Draw a rectangular area model and label the length and width.

 $2x$ $+5$ $x$ $+6$

Fill in the area model by multiplying the length and width of each box.

 $2x$ $+5$ $x$ $2x^2$ $5x$ $+6$ $12x$ $30$

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: $\left(2x + 5\right)\left(x + 6\right)$

1. $(m-3)(3m+5)$

See the help for part (a).

 $m$ $-3$ $3m$ $3m^2$ $-9m$ $+5$ $5m$ $-15$

Area as product: $\left(m − 3\right)\left(3m + 5\right)$
Area as sum: $3m^{2} − 4m − 15$

1. $(12x+1)(x^2-5)$

See the help for part (a).

 $12x$ $+1$ $x^2$ $12x^3$ $x^2$ $-5$ $-60x$ $-5$

1. $(3-5y)(2+y)$

See the help for part (a).