\(A=\left(n+10\right)\left(n+15\right)\)
\(A=n^2+15n+10n+150\)
\(A=n^2+25n+150\)
Xét: 150 là 1 số chẵn.
Xét: Nếu n chẵn:
\(n^2;25n\) luôn chẵn
\(\Rightarrow n^2+25n+150\)= chẵn+chẵn+chẵn=chẵn \(⋮2\)
Xét: Nếu n lẻ:
\(\Rightarrow n^2;25n\) luôn lẻ
\(\Rightarrow n^2+25+150\)= lẻ+lẻ+chẵn=chẵn \(⋮2\)
\(\rightarrow A⋮2\rightarrowđpcm\)
\(B=81^7-27^9-9^{13}\)
\(B=\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\)
\(B=3^{28}-3^{27}-3^{26}\)
\(B=3^2.3^{26}-3.3^{26}-3^{26}\)
\(B=3^{26}\left(3^2-3-1\right)\)
\(B=3^{26}.5⋮5\)
\(B=\left(3^2\right)^{13}.5\)
\(B=9^{13}.5⋮9\)
\(B⋮5;9\Rightarrow B⋮45\rightarrowđpcm\)
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