Bài 4 :
1) \(x^4-25x^2+20x-4\)
\(=x^2\left(x^2-25+\dfrac{20}{x}-\dfrac{4}{x^2}\right)\)
\(=x^2\left(x^2-\dfrac{4}{x^2}+\dfrac{20}{x}-25\right)\)
2) \(x^3+y^3+z^3-3xyz\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)
Bài 5 :
a) Ta có :
\(n^3-n\left(n\in Z\right)\)
\(=n\left(n^2-1\right)\)
\(=n\left(n-1\right)\left(n+1\right)\)
Vì \(n;\left(n-1\right);\left(n+1\right)\) là 3 số nguyên liên tiếp
\(\Rightarrow n\left(n-1\right)\left(n+1\right)⋮6\left(dpcm\right)\)
b) \(\left(n+6\right)^2-\left(n-6\right)^2\left(n\in Z\right)\)
\(=\left(n+6+n-6\right)\left(n+6-n+6\right)\)
\(=2n.12\)
\(=24n⋮24\left(dpcm\right)\)
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