Download MATH 1010-2: Quiz 2A

MATH 1010-2: Quiz 2A
Solution
1. (3 points) Simplify the following expression:
−3z 4 + 6z − z + 8 + z 4 − 4z 2
Solution:
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−3z 4 + 6z − z + 8 + z 4 − 4z 2
(−3)z 4 + 6z + (−1)z + 8 + 1 · z 4 + (−4)z 2
((−3) + 1)z 4 + (6 + (−1))z + 8 + (−4)z 2
(−2)z 4 + 5z + 8 + (−4)z 2
−2z 4 + 5z + 8 − 4z 2
2. (3 points) Simplify the following expression:
−3(y 2 − 2) + y 2 (y + 3)
Solution:
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−3(y 2 − 2) + y 2 (y + 3)
(−3) · (y 2 + (−2)) + y 2 (y + 3)
(−3)y 2 + (−3) · (−2) + y 2 · y + y 2 · 3
(−3)y 2 + 6 + y 3 + 3y 2
((−3) + 3)y 2 + 6 + y 3
0 · y2 + 6 + y3
6 + y3
3. (4 points) Solve the following equation and check your solution:
3(x − 4) = 7x + 6
Solution:
3(x − 4) = 7x + 6
3x − 12 = 7x + 6
3x − 12 − 7x = 7x + 6 − 7x
−4x − 12 = 6
−4x − 12 + 12 = 6 + 12
−4x = 18
¡ 1¢
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(−4x) · − 4 = 18 · − 41
x = − 92
Check:
LHS = 3 × (− 92 − 4) = − 51
2
RHS = 7 × (− 92 ) + 6 = − 51
2
Correct!
MATH 1010-2: Quiz 2B
1. (3 points) Simplify the following expression:
−3z 4 + 6z − z + 8 + z 4 − 4z 2
Solution:
=
=
=
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−3z 4 + 6z − z + 8 + z 4 − 4z 2
(−3)z 4 + 6z + (−1)z + 8 + 1 · z 4 + (−4)z 2
((−3) + 1)z 4 + (6 + (−1))z + 8 + (−4)z 2
(−2)z 4 + 5z + 8 + (−4)z 2
−2z 4 + 5z + 8 − 4z 2
2. (3 points) Simplify the following expression:
x(x2 + 3) − 3(x + 4)
Solution:
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x(x2 + 3) + (−3) · (x + 4)
x · x2 + x · 3 + (−3)x + (−3) · 4
x3 + 3x + (−3)x + (−12)
x3 + (3 + (−3))x + (−12)
x3 + 0 · x + (−12)
x3 + (−12)
x3 − 12
3. (4 points) Solve the following equation and check your solution:
12(x + 3) = 7(x + 3)
Solution:
12(x + 3) = 7(x + 3)
12x + 36 = 7x + 21
12x + 36 − 7x = 7x + 21 − 7x
5x + 36 = 21
5x + 36 − 36 = 21 − 36
5x = −15
1
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5x · = −15 ·
5
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x = −3
Check:
LHS = 12 × (−3 + 3) = 0
Correct!
RHS = 7 × (−3 + 3) = 0
Solution