Question

Chứng minh N là số chẵn

\(N=\left(a-2\right).\left(a+3\right)-\left(a-3\right).\left(a+2\right)\)(a thuộc Z)

 

Answer 1

\(N=\left(a-2\right)\left(a+3\right)-\left(a-3\right)\left(a+2\right)\)

\(\Leftrightarrow N=a\left(a-2\right)+3\left(a-2\right)-a\left(a-3\right)+2\left(a-3\right)\)

\(\Leftrightarrow N=a-2a^2+3a-6-a^2+3a+2a-6\)

\(\Leftrightarrow N=\left(a+3a+3a+2a\right)-\left(2a^2-a^2\right)-\left(6+6\right)\)

\(\Leftrightarrow N=9a-a^2-12\)

\(\Leftrightarrow N=a\left(9-a\right)-12\)

Vì \(\left[a\left(9-a\right)\right]⋮2\) và \(12⋮2\) nên \(N⋮2\)

Hay N là số chẵn (đpcm)