### Home > CC4 > Chapter 3 > Lesson 3.2.3 > Problem 3-101

3-101.

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

Review the Math Notes box in Lesson 3.2.2.

(12

*x*+ 1)(*x*− 5) = 12*x*^{2}− 59*x*− 5

See part (a).

Draw a generic rectangle and label the length and width.

(2

*x*+ 5)(*x*+ 6) = 2*x*^{2}+ 17*x*+ 30Fill in the grid by multiplying the length and width of each box.

Write an equation showing the product is the sum of the parts.

Area as a sum = 2*x*^{2}+ 12*x*+ 5*x*+ 30 = 2*x*^{2}+ 17*x*+ 30

Area as a product = (2*x*+ 5)(*x*+ 6)d.

See the help for part (c).