Algebra 1
Name: _____________________________
Sections 8.2 and 8.3
Multiplying polynomials and special products
Section 8.1 – Multiplying polynomials
Find the product.
1. x2(6x2 – 3x – 1)
2. –5a3(4a4 – 3a + 1)
3. 4d2(–2d3 + 5d2 – 6d + 2)
4. (3x + 1)(2x – 5)
5. (2y + 3)(y – 5)
6. (6a – 3)(4a – 1)
7. (b – 8)(5b – 2)
8. (8m + 7)(2m + 3)
9. (–p + 2)(3p2 + 1)
10. (2z – 7)(–z + 3)
11. (–3d + 10)(2d – 1)
12. (n + 1)(n2 + 4n + 5)
13. (w – 3)(w2 + 8w + 1)
14. (2s + 5)(s2 + 3s – 1)
15. (x2 – 4xy + y2)(5xy)
Simplify the expression.
16. a(3a + 1) + (a + 1)(a – 1)
17. (x + 2)(x + 5) – x(4x – 1)
18. (m + 7)(m – 3) + (m – 4)(m + 5)
Write a polynomial for the area of the shaded region.
19.
20.
21. Flower Bed You are designing a rectangular flower bed that you will border using
brick pavers. The width of the border around the bed will be the same on every side,
as shown.
a. Write a polynomial that represents the total area of the flower bed and the
border.
b. Find the total area of the flower bed and border when the width of the border is
1.5 feet.
Section 8.3 – Finding special products
Find the product of the square of the binomial.
1.
2.
3.
4.
5.
6.
7.
8.
9.
(x – 9)2
(m + 11)2
(5s + 2)2
(3m + 7)2
(4p – 5)2
(7a – 6)2
(10z – 3)2
(2x +y)2
(3y –x)2
Find the product of the sum and difference.
10.
11.
12.
13.
14.
15.
16.
17.
18.
(a – 9)(a + 9)
(z – 20)(z + 20)
(5r + 1)(5r – 1)
(6m + 10)(6m – 10)
(7p – 2)(7p + 2)
(9c – 1)(9c + 1)
(4x + 3)(4x – 3)
(4 – w)(4 + w)
(5 – 2y)(5 + 2y)
Answer Key
Lesson 8.2
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2.
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21.
6x4 – 3x3 – x2
–20a7 + 15a4 – 5a3
–8d5 + 20d4 – 24d3 + 8d2
6x2 – 13x – 5
2y2 – 7y– 15
24a2 – 18a + 3
5b2 – 42b + 16
16m2 + 38m + 21
–3p3 + 6p2 – p + 2
–2z2 + 13z – 21
–6d2 + 23d – 10
n3 + 5n2 + 9n + 5
w3 + 5w2 – 23w – 3
2s3 + 11s2 + 13s – 5
5x3y – 20x2y2 + 5xy3
4a2 + a – 1
–3x2 – 8x + 10
2m2 + 5m – 41
3x2 + 15x
x2 + 6x + 8
a. A = 4x2 + 22x + 30, b. 72 ft2
Lesson 8.3
1.
2.
3.
4.
5.
6.
7.
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15.
16.
17.
18.
x2 – 18x + 81
m2 + 22m + 121
25s2 + 20s + 4
9m2 + 42m + 49
16p2 – 40p + 25
49a2 – 84a + 36
100z2 – 60z + 9
4x2 + 4xy + y2
9y2 – 6xy + x2
a2 – 81
z2 – 400
25r2 – 1
36m2 – 100
49p2 – 4
81c2 – 1
16x2 – 9
16 – w2
25 – 4y2