Exercise 111 Page 130

Practice makes perfect

a We can write the area of the generic rectangle as a product by multiplying the length of the vertical side with the sum of the expressions along the horizontal side.

Product: 6(13x-21) We can also write the area of the rectangle as a sum by adding the areas contained within each of the smaller rectangles that are inside the generic rectangle.

If we calculate the products, we can get their areas.

Now we can write the area of the generic rectangle as a sum. Sum: 78x-126

b Like in Part A, we can write the area of the generic rectangle by adding the expressions along each side and then multiplying the sums.

Product: (x-5)(x+3) Next, we multiply the vertical and horizontal side of each of the smaller rectangles that are inside the generic rectangle.

If we calculate the products we can get their areas.

Now we can write the area of the generic rectangle as a sum. Sum: x^2-2x-15

c To write the area as a sum, we add the areas of the smaller rectangles that we find within the generic rectangle.

Sum: 16x^2-24x+4 To write it as a product, we must find expressions for the length of the generic rectangle's sides. We can figure this out since we know the area of the smaller rectangles within. Let's start by breaking down 16x^2, -24x, and 4 into factors.

All three expressions share 2* 2 as factors. Therefore, we can let the vertical side of the generic rectangle have a length of 4 units.

Now the horizontal side of the thee rectangles can be identified as 4x, -6, and 1 respectively.

As we can see, the generic rectangle has a width of 4 units and a length of ( 4x^2 - 6x+ 1) units. With this information, we can write the area as a product by multiplying these dimensions. Product: 4( 4x^2 - 6x+ 1)

d Like in Part A and B, the generic rectangle's area can be found if we add the expressions found along each side and then multiply these sums.

Product: (3x-2)(x+4) Finally, we should write the area as a sum, which means we need to determine the area of each small rectangle inside the generic rectangle.