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\(=8x^{3-2m}\cdot y^{6-3n}\cdot3x^{2m-1}-8x^{3-2m}\cdot y^{6-3n}\cdot\dfrac{3}{7}y^{3n-5}+8x^{3-2m}\cdot y^{6-3n}\cdot x^{2m}y^{3n}-8x^{3-2m}\cdot y^{6-3n}\cdot3y^2\)
\(=24x^2y^{6-3n}-\dfrac{24}{7}x^{3-2m}\cdot y+8x^3y^6-24x^{3-2m}\cdot y^{8-3n}\)
a: \(=24x^{2m-1+3-2m}y^{6-3m}-\dfrac{24}{7}y^{3n-7+6-3n}\cdot x^{3-2m}+8x^{3-2m+2m}\cdot y^{6-3n+3m}-24x^{3-2m}y^{6-2n+2}\)
\(=24x^2y^{6-3m}-\dfrac{24}{7}x^{3-2m}\cdot y^{-1}+8x^3y^{-3n+3m+6}-24x^{3-2m}y^{-2n+8}\)
b: \(=2x^{2n+1-2n}-6x^{2n+2-2n}+3x^{2n-1+1-2n}-9x^{2n-1+2-2n}\)
\(=2x-6x^2+3-9x\)
\(=-6x^2-7x+3\)
\(=24x^2y^{6-3n}-\dfrac{24}{7}x^{3-2m}y+8x^3y^6-24x^{3-2m}y^{8-3n}\)
Lời giải:
\((3x^{2m-1}-\frac{3}{7}y^{3n-5}+x^{2m}y^{3n}-3y^2).8x^{3-2m}y^{6-3n}\)
\(=3x^{2m-1}.8x^{3-2m}.y^{6-3n}-\frac{3}{7}y^{3n-5}.8x^{3-2m}y^{6-3n}+x^{2m}.y^{3n}.8x^{3-2m}y^{6-3n}-3y^2.8x^{3-2m}y^{6-3n}\)
\(=24x^{2m-1+3-2m}.y^{6-3n}-\frac{24}{7}y^{3n-5+6-3n}x^{3-2m}+8x^{2m+3-2m}y^{3n+6-3n}-24y^{2+6-3n}x^{3-2m}\)
\(=24x^2y^{6-3n}-\frac{24}{7}yx^{3-2m}+8x^3y^6-24y^{8-3n}x^{3-2m}\)
(x2n+xnyn+y2n)(xn−yn)(x3n+y3n)=[(xn)2+xnyn+(yn)2](xn−yn)(x3n+y3n)=(x3n−y3n)(x3n+y3n)=x6n−y6n