Question : Simplify the given expression. (a – 2b)(b – 3a) + (a + b)(a – 3b) – (b – 3a)(4a – 5b)
Option 1: 8a2 – 10ab
Option 2: 8a2 + 10ab
Option 3: 10a2 – 14ab
Option 4: 10a2 – 4ab
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Correct Answer: 10a2 – 14ab
Solution : Given: (a – 2b)(b – 3a) + (a + b)(a – 3b) – (b – 3a)(4a – 5b) = (a – 2b)(–3a + b) + (a + b)(a – 3b) – (b – 3a)(4a – 5b) = –3a2 + 6ab + ab – 2b2 + a2 + ab – 3ab – 3b2 – (4ab –12a2 – 5b2 + 15ab) = –2a2 + 5ab – 5b2 – 19ab + 12a2 + 5b2 = 10a2 – 14ab Hence, the correct answer is 10a2 – 14ab.
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Question : Simplify the following expression. 2 + (30 – 26)2 ÷ 8{3 – 2} × 0.5
Option 1: 2
Option 2: 1
Option 3: 3
Option 4: 0
Question : What is the value of (a + b)3 – a3 + b3?
Option 1: –3ab(a – b) + 2b3
Option 2: 3ab(a + b) + 2b3
Option 3: 3ab(a – b) + b3
Option 4: –3ab(a + b) + b3
Question : Simplify the given expression. 15 – (–5) × {4 – (7 – 3)} ÷ [3 × {5 + (–3) × (–6)}]
Option 1: 21
Option 2: 15
Option 3: 88
Option 4: 125
Question : What is the value of a2 + b2 + c2 – 2ab – 2bc + 2ca?
Option 1: (2a + b + c)2
Option 2: (a – b + c)2
Option 3: (a – b – 2c)2
Option 4: (a + 2b – c)2
Question : For what value of k will the expression x6 – 18x3 + k be a perfect square?
Option 1: –9
Option 2: –81
Option 3: 9
Option 4: 81
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