SECTION 5.4 Multiplying Polynomials 301
For each pair of functions, find the product. See Example 8.
- , 114. ,
115.ƒ 1 x 2 =x+ 1 , g 1 x 2 = 2 x- 3 116.ƒ 1 x 2 =x- 7 , g 1 x 2 = 4 x+ 5
ƒ 1 x 2 = 2 x g 1 x 2 = 5 x- 1 ƒ 1 x 2 = 3 x g 1 x 2 = 6 x- 81 ƒg 21 x 2117. ,
118.ƒ 1 x 2 = 3 x+ 4 , g 1 x 2 = 9 x^2 - 12 x+ 16
ƒ 1 x 2 = 2 x- 3 g 1 x 2 = 4 x^2 + 6 x+ 9Let , ,and. Find each of the following. See Example 8.
125. 126. 127.
128. 129. 130.
Perform the indicated operations. See Sections 5.1 and 5.2.
- 20 r^3 s^5
15 rs^9- 8 a^3 b^7
6 a^5 b - 9 y^11
3 y
12 p^7
6 p^3PREVIEW EXERCISES
1 ƒh2a-1
5
1 ƒh2a- b1
4
1 ƒg2a- b1
3
b1 ƒg2a-1
2
1 gh 21 - 32 1 ƒg 21 - 22 b1 ƒh 2112 1 gh 21 x 2 1 ƒh 21 - 121 ƒg 21 x 2 1 ƒh 21 x 2 1 ƒg 2122ƒ 1 x 2 =x^2 - 9 g 1 x 2 = 2 x h 1 x 2 =x- 3135.Subtract. 136.Subtract.
3 p^2 + 2 p+ 9- 4 p^2 - 8 p+ 5
5 a^2 + 3 a- 9 - 3 a^2 + 4 a- 5
EXERCISES 105–112
FOR INDIVIDUAL OR GROUP WORK
Consider the figure. Work Exercises 105–112 in order.
105.What is the length of each side of the blue square in
terms of aand b?
106.What is the formula for the area of a square? Use the
formula to write an expression, in the form of a product,
for the area of the blue square.
107.Each green rectangle has an area of. Therefore,
the total area in green is represented by the polynomial
.
108.The yellow square has an area of.
109.The area of the entire colored region is represented by , because each side
of the entire colored region has length.
110.The area of the blue square is equal to the area of the entire colored region, minus
the total area of the green squares, minus the area of the yellow square. Write this
as a simplified polynomial in aand b.- (a)What must be true about the expressions for the area of the blue square found
in Exercises 106 and 110?
(b)Write an equation based on your answer in part (a).
112.Draw a figure and give a similar proof for 1 a+b 22 =a^2 + 2 ab+b^2.
RELATING CONCEPTS
aab b