Q. If a = 1 and b = 2, what is the value of a³ + b³?
Solution
a³ + b³ = 1³ + 2³ = 1 + 8 = 9.
Correct Answer: C — 9
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Q. If a = 2 and b = 3, what is the value of (a + b)²?
Solution
(a + b)² = (2 + 3)² = 5² = 25.
Correct Answer: A — 25
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Q. If a = 3 and b = 4, what is the value of a² + b²?
Solution
a² + b² = 3² + 4² = 9 + 16 = 25.
Correct Answer: C — 25
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Q. If a = 4 and b = 5, what is the value of a² + b²?
Solution
a² + b² = 4² + 5² = 16 + 25 = 41.
Correct Answer: A — 41
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Q. If a = 5 and b = 4, what is the value of (a + b)²?
Solution
(a + b)² = (5 + 4)² = 9² = 81.
Correct Answer: C — 100
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Q. If x = 5, what is the value of (x - 1)²?
Solution
(x - 1)² = (5 - 1)² = 4² = 16.
Correct Answer: A — 16
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Q. What is the result of (a - b)(a + b)?
-
A.
a² + b²
-
B.
a² - b²
-
C.
2ab
-
D.
ab
Solution
(a - b)(a + b) = a² - b², which is the difference of squares.
Correct Answer: B — a² - b²
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Q. What is the result of (x + 1)² - (x - 1)²?
Solution
(x + 1)² - (x - 1)² = [(x² + 2x + 1) - (x² - 2x + 1)] = 4x.
Correct Answer: B — 4
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Q. What is the result of (x + y)(x - y)?
-
A.
x² + y²
-
B.
x² - y²
-
C.
2xy
-
D.
xy
Solution
(x + y)(x - y) = x² - y², which is the difference of squares.
Correct Answer: B — x² - y²
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Q. What is the value of (2x + 3)(2x - 3)?
-
A.
4x² - 9
-
B.
4x² + 9
-
C.
4x² - 6x + 9
-
D.
4x² + 6x - 9
Solution
(2x + 3)(2x - 3) = 4x² - 9.
Correct Answer: A — 4x² - 9
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Q. What is the value of (2x + 3)²?
-
A.
4x² + 9
-
B.
4x² + 12x + 9
-
C.
4x² + 6x + 9
-
D.
2x² + 6x + 9
Solution
(2x + 3)² = 4x² + 12x + 9 by expanding the square of a binomial.
Correct Answer: B — 4x² + 12x + 9
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Q. What is the value of (a + b)² - (a² + b²)?
-
A.
2ab
-
B.
a² + b²
-
C.
0
-
D.
a + b
Solution
(a + b)² - (a² + b²) = 2ab.
Correct Answer: A — 2ab
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Q. What is the value of (a + b)²?
-
A.
a² + b²
-
B.
a² + 2ab + b²
-
C.
2ab
-
D.
a² - b²
Solution
(a + b)² = a² + 2ab + b² by the expansion of the square of a binomial.
Correct Answer: B — a² + 2ab + b²
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Q. What is the value of (x + 1)(x + 2) + (x + 1)(x - 2)?
-
A.
x² + 3x + 2
-
B.
x² + 3x - 2
-
C.
2x² + 2
-
D.
2x² + 3x
Solution
(x + 1)((x + 2) + (x - 2)) = (x + 1)(2x) = 2x² + 2x.
Correct Answer: C — 2x² + 2
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Q. What is the value of (x + 1)(x - 1)?
-
A.
x² + 1
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B.
x² - 1
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C.
x² - 2
-
D.
1 - x²
Solution
(x + 1)(x - 1) = x² - 1, which is the difference of squares.
Correct Answer: B — x² - 1
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Q. What is the value of (x + 2)(x - 2)?
-
A.
x² + 4
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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. Which identity represents the difference of squares?
-
A.
(a + b)² = a² + 2ab + b²
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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
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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 - y)³?
-
A.
x³ - 3x²y + 3xy² - y³
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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 (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 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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