Question

C/M Rằng:\(\left(2n+5\right)^2-25\) chia hết cho 4,với mọi n thuộc Z

Answer 1

\(\left(2n+5\right)^2-25=\left(2n+5\right)^2-5^2=\left(2n+5-5\right)\left(2n+5+5\right)=2n\left(2n+10\right)=4n^2+20n\)

Vì: \(\left\{{}\begin{matrix}4n^2⋮4\\20n⋮4\end{matrix}\right.\)\(\Rightarrow4n^2+20n⋮4\left(đpcm\right)\)

Answer 2

Ta có: A=(2n+5)2−25

\(2^2.n^2+25-25=4.n^2⋮4\)

⇒A⋮4(đpcm)