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 = 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. What is the result of (a - b)(a + b)?
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A.
a² + b²
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B.
a² - b²
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C.
2ab
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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 + y)(x - y)?
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A.
x² + y²
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B.
x² - y²
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C.
2xy
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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)²?
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A.
4x² + 9
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B.
4x² + 12x + 9
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C.
4x² + 6x + 9
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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?
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A.
a² + b²
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B.
a² + 2ab + b²
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C.
2ab
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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 - 1)?
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A.
x² + 1
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B.
x² - 1
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C.
x² - 2
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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. Which identity represents the expansion of (a + b + c)²?
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A.
a² + b² + c² + 2ab + 2bc + 2ca
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B.
a² + b² + c² + 3abc
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C.
a² + b² + c²
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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?
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A.
x³ - 3x²y + 3xy² - y³
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B.
x³ - y³
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C.
x³ - 3xy² + 3x²y - y³
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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 identity for (x + y)³?
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A.
x³ + y³ + 3xy(x + y)
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B.
x³ + y³ - 3xy(x + y)
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C.
x³ + y³ + 3xy²
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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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