\(\left(x^2-x-2\right)^2+\left(x-2\right)^2\)
\(=x^4-2x^3-3x^2+4x+4+x^2-4x+4\)
\(=x^4-2x^3-2x^2+8\)
\(=x^3\left(x-2\right)-2\left(x^2-4\right)\)
\(=x^3\left(x-2\right)-2\left(x-2\right)\left(x+2\right)\)
\(=\left(x-2\right)\left(x^3-2x-4\right)\)
\(=\left(x-2\right)\left[x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\right]\)
\(=\left(x-2\right)\left(x-2\right)\left(x^2+2x+2\right)\)
\(=\left(x-2\right)^2\left(x^2+2x+2\right)\)
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Câu a):
ta có (x2-x-2)2+(x-2)2
=((x-2)2(x+1))2+(x-2)2
=(x-2)2(x2+2x+2)
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