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a: \(=n^3+2n^2+3n^2+6n-n-2-n^3+5\)
\(=5n^2+5n+3⋮̸5\)
b:\(=6n^2+30n+n+5-6n^2+3n-10n+5\)
\(=24n+10=2\left(12n+5\right)⋮2\)
d: \(=4x^2y^2-2x^2y+2xy^2-xy-4x^2y^2+xy\)
\(=-2\left(x^2y-xy^2\right)⋮2\)
(x2n+xnyn+y2n)(xn-yn)(x3n+y3n)
\(=\text{[}\left(x^n\right)^2+x^ny^n+\left(y^n\right)^2\text{]}\left(x^n-y^n\right)\left(x^{3n}+y^{3n}\right)\)
\(=\left[\left(x^n\right)^3-\left(y^n\right)^3\right]\left(x^{3n}+y^{3n}\right)\)
\(=\left[x^{3n}-y^{3n}\right]\left(x^{3n}+y^{3n}\right)\)
\(=\left(x^{3n}\right)^2-\left(y^{3n}\right)^2\)
\(=x^{6n}-y^{6n}\)
a) \(\left(a-b\right)^2-2\left(a-b\right)c+c^2\)
\(=\left(a-b-c\right)^2\)
b) \(81a^2+18a+1\)
\(=\left(9a\right)^2+2.9a.1+1^2\)
\(=\left(9a+1\right)^2\)
c) \(3\left(x+1\right)^n.y-6\left(x+1\right)^{n+1}\)
\(=3\left(x+1\right)^n.y-6\left(x+1\right)^n.6\left(x+1\right)\)
\(=3\left(x+1\right)^n\left[y-12\left(x+1\right)\right]\)
\(=3\left(x+1\right)^n\left(y-12x-12\right)\)
d) \(\left(a-2b\right)^{3n}+\left(a-2b\right)^{3n+1}\)
\(=\left(a-2b\right)^{3n}+\left(a-2b\right)^{3n}.\left(a-2b\right)\)
\(=\left(a-2b\right)^{3n}\left(1+a-2b\right)\)
tìm số tự nhiên n
a) x5 : xn
b) x2n : x5
c) 3x5yn : 2ny3
d) xn+2y3 : x5y3
e) x3n+1 : x7
f) xnyn+3 : x6y10
a: \(4x^2\left(3x^{n+1}-2x^n\right)\)
\(=12x^{n+3}-8x^{n+2}\)
b: \(=2x^{2n}+4x^ny^n+2y^{2n}-4x^ny^n-2y^{2n}\)
\(=2x^{2n}\)
c: \(=\left(x^{3n}-y^{3n}\right)\left(x^{3n}+y^{3n}\right)=x^{6n}-y^{6n}\)
d: \(=4^n\cdot4-3\cdot4^n=4^n\)
Ta có: \(\left(x^{3n}+y^{3n}\right)\left(x^{3n}-y^{3n}\right)=-x^{6n}-y^{6n}\)
\(\Leftrightarrow x^{6n}-y^{6n}=-x^{6n}-y^{6n}\)
\(\Leftrightarrow n\in\varnothing\)