Question
Download Solution PDFSimplify the following expression:
\(\frac{(8.25)^3-3 \times(8.25)^2 \times 0.25+24.75 \times(0.25)^2-(0.25)^3}{4 \times 4 \times 4}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Simplify the following expression:
\(\dfrac{(8.25)^3-3 \times(8.25)^2 \times 0.25+24.75 \times(0.25)^2-(0.25)^3}{4 \times 4 \times 4}\)
Formula used:
(a - b)3 = a3 - 3a2b + 3ab2 - b3
Calculation:
\(\dfrac{(8.25)^3-3 \times(8.25)^2 \times 0.25+24.75 \times(0.25)^2-(0.25)^3}{4 \times 4 \times 4}\)
Let a = 8.25 and b = 0.25
⇒ a3 - 3a2b + 3ab2 - b3 = (8.25 - 0.25)3
⇒ (8.25 - 0.25)3 = 83
⇒ 83 = 512
⇒ \(\dfrac{512}{4 \times 4 \times 4}\)
⇒ \(\dfrac{512}{64}\)
⇒ 8
∴ The correct answer is option (4).
Last updated on Jun 3, 2025
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