Question
Download Solution PDFWhat is the value of (27x3 - 58x2y + 31xy2 - 8y3), when x = -5 and y = -7?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
(3x - 2y)3 = (3x)3 - (2y)3 - 3 × (3x)2 × (2y) + 3 × 3x × (2y)2
⇒ 27x3 - 8y3 - 54x2y - 4x2y + 36 xy2 - 5xy2 = (3x - 2y)3 - 4x2y - 5xy2
⇒ 27x3 - 58x2y + 31xy2 - 8y3 = (3x - 2y)3 - 4x2y - 5xy2
Now we put the value of x = - 5 and y = - 7
(3x - 2y)3 - 4x2y - 5xy2
⇒ {3 × (- 5) - 2 × (- 7)}3 - 4 × (- 5)2 × (- 7) - 5 × (- 5) × (- 7)2
⇒ {- 15 + 14}3 + 4 × 25 × 7 + 25 × 49
⇒ (-1)3 + 700 + 1225
⇒ 1925 - 1 = 1924
∴ The correct answer is 1924.
Last updated on Jul 8, 2025
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