Question:
Find the value of \(p^3-27q^3\) if \(p-3q=-7\) and \(pq=-10\).
Find the value of \(p^3-27q^3\) if \(p-3q=-7\) and \(pq=-10\).
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\(a^3-b^3=(a-b)^3+3ab(a-b)\)
Updated On: Apr 21, 2026
- \(-133\)
- 973
- 287
- \(-553\)
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Identify the identity.
\(a^3 - b^3 = (a-b)^3 + 3ab(a-b)\).
Let \(a = p\), \(b = 3q\). Then \(p^3 - (3q)^3 = p^3 - 27q^3\). Step 2: Extract given values.
\(p - 3q = -7\).
\(p \times 3q = 3pq = 3 \times (-10) = -30\). Step 3: Apply the identity.
\(p^3 - 27q^3 = (-7)^3 + 3(-30)(-7)\). Step 4: Compute.
\((-7)^3 = -343\).
\(3 \times (-30) \times (-7) = 3 \times 210 = 630\).
Sum = \(-343 + 630 = 287\).
\(a^3 - b^3 = (a-b)^3 + 3ab(a-b)\).
Let \(a = p\), \(b = 3q\). Then \(p^3 - (3q)^3 = p^3 - 27q^3\). Step 2: Extract given values.
\(p - 3q = -7\).
\(p \times 3q = 3pq = 3 \times (-10) = -30\). Step 3: Apply the identity.
\(p^3 - 27q^3 = (-7)^3 + 3(-30)(-7)\). Step 4: Compute.
\((-7)^3 = -343\).
\(3 \times (-30) \times (-7) = 3 \times 210 = 630\).
Sum = \(-343 + 630 = 287\).
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