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\(=8x^{3-2m}\cdot y^{6-3n}\cdot3x^{2m-1}-8x^{3-2m}\cdot y^{6-3n}\cdot\dfrac{3}{7}y^{3n-5}+8x^{3-2m}\cdot y^{6-3n}\cdot x^{2m}y^{3n}-8x^{3-2m}\cdot y^{6-3n}\cdot3y^2\)
\(=24x^2y^{6-3n}-\dfrac{24}{7}x^{3-2m}\cdot y+8x^3y^6-24x^{3-2m}\cdot y^{8-3n}\)
Bài làm :
\(a,\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)+10\)
\(=8x+16-5x^2-10x+\left(4x-8\right)\left(x+1\right)+2\left(x^2-2^2\right)+10\)
\(=8x+16-5x^2-10x+4x^2+4x-8x-8+2x^2-8+10\)
\(=\left(8x-10x+4x-8x\right)+\left(-5x^2+4x^2+2x^2\right)+\left(16-8-8+10\right)\)
\(=-6x+x^2+10\)
a)\(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)+10\)\(=8x+16-5x^2-2+4x-8x-8+2x-4x-4+10\)\(=\left(8x+4x-8x+2x-4x\right)+\left(16-2-8-4+10\right)+5x^2\)
\(=2x+12+5x^2\)
b)\(4\left(x-1\right)\left(x+5\right)-\left(x+2\right)\left(x+5\right)-3\left(x-1\right)\left(x+2\right)\)
\(=4x-4x-20-\left[x^2+5x+2x+10\right]-3\left[x^2+2x-1x-2\right]\)
\(=4x-4x-20-x^2-5x-2x-10-3x^2-6x+3x+6\)
\(=\left(4x-4x-5x-2x-6x+3x\right)+\left(-20-10+6\right)+\left(-x^2-3x^2\right)\)
\(=-10x-24-4x^2\)
c)\(\left(x^{2n}+x^ny^n+y^{2n}\right)\left(x^n-y^n\right)\left(x^{3n}+y^{3n}\right)\)
Xét tích \(\left(x^{2n}+x^ny^n+y^{2n}\right)\left(x^n-y^n\right)\Leftrightarrow\left(x^n\right)^3-\left(y^n\right)^3=x^{3n}-y^{3n}\)
Thay vào bt đã cho ta có \(\left(x^{3n}-y^{3n}\right)\left(x^{3n}+y^{3n}\right)\)
\(\Leftrightarrow\left(x^{3n}\right)^2-\left(y^{3n}\right)^2=x^{6n}-y^{6n}\)