\(a,\left(n+2\right)^2-\left(n-2\right)^2\)
\(=\left(n+2-n+2\right)\left(n+2+n-2\right)\)
\(=4.2n=8n⋮8\)
\(b,\left(n+7\right)^2-\left(n-5\right)^2\)
\(=\left(n+7-n+5\right)\left(n+7+n-5\right)\)
\(=12.\left(2+2n\right)=24+24n⋮24\)
\(\left(n+2\right)^2-\left(n-2\right)^2\)
\(=n^2+4n+4-\left(n^2-4n+4\right)\)
\(=n^2+4n+4-n^2+4n-4\)
\(=8n⋮8\left(đpcm\right)\)
\(\left(n+7\right)^2-\left(n-5\right)^2\)
\(=n^2+14n+49-\left(n^2-10n+25\right)\)
\(=n^2+14n+49-n^2+10n-25\)
\(=24n+24\)
\(=24\left(n+1\right)⋮24\left(đpcm\right)\)
\(\left(x-3\right)^3-\left(x-4\right)^3\)
\(=\left(x-3-x+4\right)\left[\left(x-3\right)^2+\left(x-3\right)\left(x-4\right)+\left(x-4\right)^2\right]\)
\(=x^2-6x+9+x^2-7x+12+x^2-8x+16\)
\(=3x^2-21x+37\)
\(\left(2x-1\right)\left(3x-2\right)-\left(x+2\right)\left(x-3\right)\)
\(=6x^2-4x-3x+2-x^2+x+6\)
\(=5x^2-6x+8\)
