CPM Homework Help : CCG Problem 5-22

Multiply each polynomial. That is, change each product to a sum.

$(2x+1)(3x-2)$

Step 1(a):

Draw a generic rectangle. Place the $(2x+1)$ as one side of the rectangle and $(3x-2)$ as another side of the rectangle.

left edge top $+1$

interior top left blank $\space$

interior top right blank $\space$

left edge bottom $2x$

interior bottom left blank $\space$

interior bottom right blank $\space$

bottom edge left $3x$

bottom edge right $-2$

Step 2(a):

Find the area of each part of the rectangle by multiplying $\left(\text{base}\times\text{height}\right)$ . Then combine like terms.

Answer (a):

$(2x+1)(3x-2)=6x^2-x-2$

$(2x+1)(3x^2-2x-5)$
Hint (b):
Follow the same steps from part (a), but your generic rectangle will have six boxes instead of four.