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1. Simplify : $\frac{{1.5}^{3} + {4.7}^{3} + {3.8}^{3} - 3 \times 1.5 \times 4.7 \times 3.8}{{1.5}^{2} + {4.7}^{2} + {3.8}^{2} - 1.5 \times 4.7 - 4.7 \times 3.8 - 3.8 \times 1.5}$ = ?

A. 0

B. 1

C. 10

D. 30

Solution:

\frac{{1.5}^{3} + {4.7}^{3} + {3.8}^{3} - 3 \times 1.5 \times 4.7 \times 3.8}{{1.5}^{2} + {4.7}^{2} + {3.8}^{2} - 1.5 \times 4.7 - 4.7 \times 3.8 - 3.8 \times 1.5}

= \frac{(1.5 + 4.7 + 3.8) {{1.5}^{2} + {4.7}^{2} + {3.8}^{2} - 1.5 \times 4.7 - 4.7 \times 3.8 - 3.8 \times 1.5}}{{{1.5}^{2} + {4.7}^{2} + {3.8}^{2} - 1.5 \times 4.7 - 4.7 \times 3.8 - 3.8 \times 1.5}}

[∴ a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)]

\begin{aligned} = 1.5 + 4.7 + 3.8 \\ = 10.0 \\ = 10 \end{aligned}

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