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a: \(=12x^{n+2}+4x^2-8x^{n+2}\)
\(=4x^{n+2}+4x^2\)
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: \(=4^n\cdot4-3\cdot4^n=4^n\)
a: \(4x^2\left(3x^{n+1}-2x^n\right)\)
\(=4x^2\cdot3x^{n+1}-4x^2\cdot2x^n\)
\(=12x^{n+3}-8x^{n+2}\)
b: \(2\left(x^{2n}+2x^ny^n+y^{2n}\right)-y^n\left(4x^n+2y^n\right)\)
\(=2x^{2n}+4x^ny^n+2y^{2n}-4x^ny^n-2y^{2n}\)
\(=2x^{2n}\)
c: \(=\left(x^{3n}-y^{3n}\right)\left(x^{3n}+y^{3n}\right)\)
\(=x^{6n}-y^{6n}\)
d: \(=4^n\cdot4-3\cdot4^n=4^n\)
a: 4x2(3xn+1−2xn)4x2(3xn+1−2xn)
=4x2⋅3xn+1−4x2⋅2xn=4x2⋅3xn+1−4x2⋅2xn
=12xn+3−8xn+2=12xn+3−8xn+2
b: 2(x2n+2xnyn+y2n)−yn(4xn+2yn)2(x2n+2xnyn+y2n)−yn(4xn+2yn)
=2x2n+4xnyn+2y2n−4xnyn−2y2n=2x2n+4xnyn+2y2n−4xnyn−2y2n
=2x2n=2x2n
c: =(x3n−y3n)(x3n+y3n)=(x3n−y3n)(x3n+y3n)
=x6n−y6n=x6n−y6n
d: =4n⋅4−3⋅4n=4n
a) \(15x^ny^{2n}-3x^{n+1}\left(-y\right)^{2n}\)
\(=x^ny^{2n}\left(15-3x\right)\)
\(=3x^ny^{2n}\left(5-x\right)\)
b) \(4x^{2n}y^{n-1}+2\left(-x\right)^{2n+1}y^n\)
\(=4x^{2n}y^{n-1}-2x^{2n+1}y^n\)
\(=2x^{2n}y^{n-1}\left(2-xy\right)\)
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: \(=4^n\cdot4-3\cdot4^n=4^n\)
Bài 1:
Ta có:
\(a+b+c=0\\ \Leftrightarrow a^3+b^3+c^3+3\left(a^2b+a^2c+b^2a+b^2c+c^2a+c^2b+2abc\right)=0\\ \Leftrightarrow a^3+b^3+c^3+3\left(a+b\right)\left(b+c\right)\left(c+a\right)=0\\ \Leftrightarrow a^3+b^3+c^3-3abc=0\\ \Leftrightarrow a^3+b^3+c^3=3abc\left(dpcm\right)\)