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Question Number 8050 by Chantria last updated on 28/Sep/16

$$\mathrm{The}\mathrm{value}\mathrm{of}$$$$\frac{{18}^3+7^3+3\cdot 18\cdot 7\cdot 25}{3^6+6\cdot 243\cdot 2+15\cdot 181\cdot 4+20\cdot 27\cdot 8+15\cdot 9\cdot 16+6\cdot 3\cdot 32+64}$$$$\mathrm{is}$$

Answered by sandy_suhendra last updated on 28/Sep/16

$$=\frac{{(18+7)}^3}{{(3+2)}^6}=\frac{{25}^3}{5^6}=\frac{5^6}{5^6}=1$$$$using:$$$${(a+b)}^3=a^3+b^3+3ab(a+b)$$$${(a+b)}^6=a^6+6a^{5}b+15a^4{b}^2+20a^3{b}^3+15a^2{b}^4+6{ab}^5+b^6$$

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