Q. What is the value of (x + 2)(x - 2)?
-
A.
x² + 4
-
B.
x² - 4
-
C.
2x
-
D.
x² - 2
Solution
(x + 2)(x - 2) = x² - 4 by the difference of squares identity.
Correct Answer:
B
— x² - 4
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Q. What is the value of (x + 2)² - (x² + 4)?
-
A.
0
-
B.
4
-
C.
2x
-
D.
x² + 2
Solution
(x + 2)² = x² + 4x + 4; thus, (x + 2)² - (x² + 4) = 4x.
Correct Answer:
C
— 2x
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Q. What is the value of (x + 3)(x - 3)? (2023)
-
A.
x² + 9
-
B.
x² - 9
-
C.
3x
-
D.
x² - 6
Solution
(x + 3)(x - 3) = x² - 9 by the difference of squares formula.
Correct Answer:
B
— x² - 9
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Q. What is the value of (x + y + z)²?
-
A.
x² + y² + z²
-
B.
x² + y² + z² + 2xy + 2yz + 2zx
-
C.
x² + y² + z² + 3xyz
-
D.
x² + y² + z² - 2xy - 2yz - 2zx
Solution
(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx by the expansion of the square of a trinomial.
Correct Answer:
B
— x² + y² + z² + 2xy + 2yz + 2zx
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Q. What is the value of (x + y)(x - y)?
-
A.
x² + y²
-
B.
x² - y²
-
C.
2xy
-
D.
xy
Solution
(x + y)(x - y) = x² - y² by the difference of squares identity.
Correct Answer:
B
— x² - y²
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Q. What is the value of (x - 4)(x + 4)?
-
A.
x² - 16
-
B.
x² + 16
-
C.
x² - 8
-
D.
x² + 8
Solution
(x - 4)(x + 4) = x² - 16.
Correct Answer:
A
— x² - 16
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Q. Which identity represents the difference of squares?
-
A.
(a + b)² = a² + 2ab + b²
-
B.
(a - b)² = a² - 2ab + b²
-
C.
a² - b² = (a + b)(a - b)
-
D.
a² + b² = (a + b)² - 2ab
Solution
The difference of squares is given by a² - b² = (a + b)(a - b).
Correct Answer:
C
— a² - b² = (a + b)(a - b)
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Q. Which identity represents the expansion of (a + b + c)²?
-
A.
a² + b² + c² + 2ab + 2bc + 2ca
-
B.
a² + b² + c² + 3abc
-
C.
a² + b² + c²
-
D.
2a² + 2b² + 2c²
Solution
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.
Correct Answer:
A
— a² + b² + c² + 2ab + 2bc + 2ca
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Q. Which of the following is the correct expansion of (x - 3)²?
-
A.
x² - 6x + 9
-
B.
x² + 6x + 9
-
C.
x² - 9
-
D.
x² - 3
Solution
(x - 3)² = x² - 2(3)x + 3² = x² - 6x + 9.
Correct Answer:
A
— x² - 6x + 9
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Q. Which of the following is the correct expansion of (x - y)³?
-
A.
x³ - 3x²y + 3xy² - y³
-
B.
x³ - y³
-
C.
x³ - 3xy² + 3x²y - y³
-
D.
3x²y - 3xy²
Solution
(x - y)³ = x³ - 3x²y + 3xy² - y³ by the binomial theorem.
Correct Answer:
A
— x³ - 3x²y + 3xy² - y³
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Q. Which of the following is the correct factorization of a² - b²?
-
A.
(a + b)(a - b)
-
B.
(a - b)(a - b)
-
C.
(a + b)(a + b)
-
D.
a² - 2ab + b²
Solution
a² - b² = (a + b)(a - b) by the difference of squares identity.
Correct Answer:
A
— (a + b)(a - b)
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Q. Which of the following is the correct identity for (a - b)(a + b)? (2019)
-
A.
a² + b²
-
B.
a² - b²
-
C.
ab
-
D.
a - b
Solution
(a - b)(a + b) = a² - b² by the difference of squares formula.
Correct Answer:
B
— a² - b²
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Q. Which of the following is the correct identity for (a - b)²?
-
A.
a² - 2ab + b²
-
B.
a² + 2ab + b²
-
C.
a² - b²
-
D.
2a² - 2b²
Solution
(a - b)² = a² - 2ab + b² by the expansion of the square of a binomial.
Correct Answer:
A
— a² - 2ab + b²
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Q. Which of the following is the correct identity for (x + y + z)³?
-
A.
x³ + y³ + z³ + 3(x + y)(y + z)(z + x)
-
B.
x³ + y³ + z³ + 3xyz
-
C.
x³ + y³ + z³ + 3xy + 3yz + 3zx
-
D.
x³ + y³ + z³ - 3xyz
Solution
(x + y + z)³ = x³ + y³ + z³ + 3xyz.
Correct Answer:
B
— x³ + y³ + z³ + 3xyz
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Q. Which of the following is the correct identity for (x + y)³?
-
A.
x³ + y³ + 3xy(x + y)
-
B.
x³ + y³ - 3xy(x + y)
-
C.
x³ + y³ + 3xy²
-
D.
x³ - y³
Solution
(x + y)³ = x³ + y³ + 3xy(x + y) by the binomial expansion.
Correct Answer:
A
— x³ + y³ + 3xy(x + y)
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Q. Which of the following is the expanded form of (x + 2)²?
-
A.
x² + 4
-
B.
x² + 4x + 4
-
C.
x² + 2x + 2
-
D.
x² + 2
Solution
(x + 2)² = x² + 2*2*x + 2² = x² + 4x + 4.
Correct Answer:
B
— x² + 4x + 4
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Q. Which of the following is true for the identity (a + b)³?
-
A.
a³ + b³
-
B.
a³ + 3a²b + 3ab² + b³
-
C.
a² + b²
-
D.
3ab
Solution
(a + b)³ = a³ + 3a²b + 3ab² + b³.
Correct Answer:
B
— a³ + 3a²b + 3ab² + b³
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Q. Which of the following is true for the identity (x + y)²?
-
A.
x² + y²
-
B.
x² + 2xy + y²
-
C.
x² - 2xy + y²
-
D.
2xy
Solution
(x + y)² = x² + 2xy + y².
Correct Answer:
B
— x² + 2xy + y²
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Q. Which of the following represents the identity for (a + b + c)²?
-
A.
a² + b² + c² + 2ab + 2bc + 2ca
-
B.
a² + b² + c² + 3abc
-
C.
a² + b² + c²
-
D.
a² + b² + c² + ab + ac + bc
Solution
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.
Correct Answer:
A
— a² + b² + c² + 2ab + 2bc + 2ca
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Showing 31 to 49 of 49 (2 Pages)
