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x8 + x +1= x8 +x7 - x7 + x6 - x6 + x5 - x5 + x4 -x4 +x3 -x3 + x2 -x2 +x +1
= (x2+x+1)*(x6 -x5+x3-x2+1)
\(x^8y^8+x^4y^4+1\)
\(=\left(x^4y^4\right)^2+2x^4y^4+1-x^4y^4\)
\(=\left(x^4y^4+1\right)^2-\left(x^2y^2\right)^2\)
\(=\left(x^4y^4-x^2y^2+1\right)\left(x^4y^4+x^2y^2+1\right)\)
\(=\left(x^4y^4-x^2y^2+1\right)\left[\left(x^2y^2+1\right)^2-\left(xy\right)^2\right]\)
\(=\left(x^4y^4-x^2y^2+1\right)\left(x^2y^2-xy+1\right)\left(x^2y^2+xy+1\right)\)
Chúc bạn học tốt.
Ta có:
\(x^9-x^7-x^6-x^5+x^4+x^3+x^2-1\)
\(=\left(x^9-x^8\right)+\left(x^8-x^7\right)-\left(x^6-x^5\right)-\left(2x^5-2x^4\right)-\left(x^4-x^3\right)+\left(x^2-x\right)+\left(x-1\right) \)
\(=x^8.\left(x-1\right)+x^7.\left(x-1\right)-x^5.\left(x-1\right)-2x^4.\left(x-1\right)-x^3\left(x-1\right)+x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(x^8+x^7-x^5-2x^4-x^3+x+1\right)\)
\(x^8+x^7+1=x^8+x^7+x^6-x^6-x^5-x^4+x^5+x^4+x^3-x^3-x^2-x+x^2+x+1\)
\(=x^6\left(x^2+x+1\right)-x^4\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)