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If (p - q) = 8, then what is the value of q3 - p3 + 24pq?
- a)729
- b)512
- c)-512
- d)-343
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If (p - q) = 8, then what is the value of q3 - p3 + 24pq?a)729b)512c)-...
Given:
(p - q) = 8,
Formula used:
(a - b)3 = a3 - b3 - 3ab(a - b)
Calculation:
According to the question,
⇒ (p - q) = 8
Take cube on both sides,
⇒ (p - q)3 = 83
⇒ p3 - q
3
- 3pq(p - q)= 83
⇒ p
3
- q3
- 3pq(8) = 512⇒ p
3
- q3
- 24pq = 512It can be written as:
⇒ q
3
- p
3
+ 24pq = -512Therefore, "-512" is the required answer.
Most Upvoted Answer
If (p - q) = 8, then what is the value of q3 - p3 + 24pq?a)729b)512c)-...
Explanation:
Given:
(p - q) = 8
To Find:
q^3 - p^3 + 24pq
Step 1: Express p and q in terms of p - q
From the given equation:
p = q + 8
Step 2: Substitute p and q in the expression q^3 - p^3 + 24pq
q^3 - (q + 8)^3 + 24(q + 8)q
Step 3: Simplify the expression
q^3 - (q^3 + 3q^2*8 + 3q*8^2 + 8^3) + 24(q^2 + 8q)
q^3 - q^3 - 192q^2 - 192q - 512 + 24q^2 + 192q
-192q^2 - 512 + 24q^2
-168q^2 - 512
Step 4: Combine like terms and simplify further
-144q^2 - 512
Therefore, the value of q^3 - p^3 + 24pq when (p - q) = 8 is -512.
So, the correct answer is option C) -512.
Given:
(p - q) = 8
To Find:
q^3 - p^3 + 24pq
Step 1: Express p and q in terms of p - q
From the given equation:
p = q + 8
Step 2: Substitute p and q in the expression q^3 - p^3 + 24pq
q^3 - (q + 8)^3 + 24(q + 8)q
Step 3: Simplify the expression
q^3 - (q^3 + 3q^2*8 + 3q*8^2 + 8^3) + 24(q^2 + 8q)
q^3 - q^3 - 192q^2 - 192q - 512 + 24q^2 + 192q
-192q^2 - 512 + 24q^2
-168q^2 - 512
Step 4: Combine like terms and simplify further
-144q^2 - 512
Therefore, the value of q^3 - p^3 + 24pq when (p - q) = 8 is -512.
So, the correct answer is option C) -512.
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If (p - q) = 8, then what is the value of q3 - p3 + 24pq?a)729b)512c)-512d)-343Correct answer is option 'C'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about If (p - q) = 8, then what is the value of q3 - p3 + 24pq?a)729b)512c)-512d)-343Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (p - q) = 8, then what is the value of q3 - p3 + 24pq?a)729b)512c)-512d)-343Correct answer is option 'C'. Can you explain this answer?.
If (p - q) = 8, then what is the value of q3 - p3 + 24pq?a)729b)512c)-512d)-343Correct answer is option 'C'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about If (p - q) = 8, then what is the value of q3 - p3 + 24pq?a)729b)512c)-512d)-343Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (p - q) = 8, then what is the value of q3 - p3 + 24pq?a)729b)512c)-512d)-343Correct answer is option 'C'. Can you explain this answer?.
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