# Download Find each product. 6. c d (5cd − 3c d − 4d ) SOLUTION: Simplify

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```7-6 Mulitplying a Polynomial by a Monomial
Find each product.
2 3
7
3 2
3
6. c d (5cd − 3c d − 4d )
SOLUTION: Simplify each expression.
2
8. x(3x + 4) + 2(7x − 3)
SOLUTION: 2
2
2
4
2
10. −5w (8w x − 11wx ) + 6x(9wx − 4w − 3x )
SOLUTION: Solve each equation.
12. −6(11 − 2c) = 7(−2 − 2c)
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7-6 Mulitplying a Polynomial by a Monomial
Solve each equation.
12. −6(11 − 2c) = 7(−2 − 2c)
SOLUTION: 14. −2(w + 1) + w = 7 − 4w
SOLUTION: 16. a(a + 3) + a(a − 6) + 35 = a(a − 5) + a(a + 7)
SOLUTION: Find each product.
2
18. b(b − 12b + 1)
SOLUTION: Page 2
7-6 Mulitplying a Polynomial by a Monomial
Find each product.
2
18. b(b − 12b + 1)
SOLUTION: 3
3
2
20. −3m (2m − 12m + 2m + 25)
SOLUTION: 2
2
22. 2pr (2pr + 5p r − 15p )
SOLUTION: Simplify each expression.
2
24. −3(5x + 2x + 9) + x(2x − 3)
SOLUTION: 2
26. −4d(5d − 12) + 7(d + 5)
SOLUTION: Page 3
7-6 Mulitplying a Polynomial by a Monomial
2
26. −4d(5d − 12) + 7(d + 5)
SOLUTION: 2 2
2
2 2
2
28. 2j (7j k + j k + 5k) − 9k(−2j k + 2k + 3j )
SOLUTION: 30. DAMS A new dam being built has the shape of a trapezoid. The base at the bottom of the dam is 2 times the
height. The base at the top of the dam is
times the height minus 30 feet.
a. Write an expression to find the area of the trapezoidal cross section of the dam.
b. If the height of the dam is 180 feet, find the area of this cross section.
SOLUTION: a. The equation for the area of a trapezoid is
eSolutions
b 1 = 2h
.
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7-6 Mulitplying a Polynomial by a Monomial
30. DAMS A new dam being built has the shape of a trapezoid. The base at the bottom of the dam is 2 times the
height. The base at the top of the dam is
times the height minus 30 feet.
a. Write an expression to find the area of the trapezoidal cross section of the dam.
b. If the height of the dam is 180 feet, find the area of this cross section.
SOLUTION: a. The equation for the area of a trapezoid is
.
b 1 = 2h
b2 =
b. Let h = 180.
So, the area is 32,940 square feet.
Simplify each expression.
2
2
3
2
3
2 3
2
40. −x z(2z + 4xz ) + xz (xz + 5x z) + x z (3x z + 4xz)
SOLUTION: Page 5
7-6 Mulitplying
a Polynomial by a Monomial
So, the area is 32,940 square feet.
Simplify each expression.
2
2
3
2
3
2 3
2
40. −x z(2z + 4xz ) + xz (xz + 5x z) + x z (3x z + 4xz)
SOLUTION: 42. PETS Che is building a dog house for his new puppy. The upper face of the dog house is a trapezoid. If the height
of the trapezoid is 12 inches, find the area of the face of this piece of the dog house.
SOLUTION: The formula for the area of a trapezoid is
.
Now substitute h = 12 inches into the equation.
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7-6 Mulitplying a Polynomial by a Monomial
42. PETS Che is building a dog house for his new puppy. The upper face of the dog house is a trapezoid. If the height
of the trapezoid is 12 inches, find the area of the face of this piece of the dog house.
SOLUTION: The formula for the area of a trapezoid is
.
Now substitute h = 12 inches into the equation.
Therefore, the area of the trapezoid is 318 square inches.
52. If a = 5x + 7y and b = 2y − 3x, what is a + b?
F 2x − 9y
G 3y + 4x
H 2x + 9y
J 2x − 5y
SOLUTION: So, the correct choice is H.
54. SHORT RESPONSE Write an equation in which x varies directly as the cube of y and inversely as the square of
z.
SOLUTION: If x varies directly as the cube of y, then both x and y must be in the numerators on either side of the equal sign.
When x varies inversely with the square of z. then the z must be in the denominator. Then
combination of the two is
Page 7
.
7-6 Mulitplying a Polynomial by a Monomial
So, the correct choice is H.
54. SHORT RESPONSE Write an equation in which x varies directly as the cube of y and inversely as the square of
z.
SOLUTION: If x varies directly as the cube of y, then both x and y must be in the numerators on either side of the equal sign.
When x varies inversely with the square of z. then the z must be in the denominator. Then
. The combination of the two is
.
Find each sum or difference.
2
2
56. (3z + 2z − 1) + (z − 6)
SOLUTION: 3
2
3
60. (8c − 3c + c − 2) − (3c + 9)
SOLUTION: Find the degree of each polynomial.
62. −10
SOLUTION: A constant has a degree of 0.
3
64. 9a − 8a + 6
SOLUTION: The degree of a polynomial is the greatest degree of any term in the polynomial.
Find the degree of each term:
9a: degree 1
3
−8a : degree 3
6: degree 0
The degree of the polynomial is 3.
4 52
66. −3p r t
SOLUTION: To find the degree of monomial, add the degrees of each variable: 4 + 5 + 2 = 11.
Write an equation in function notation for each relation.