Odpowiedź:
[tex]a)\ \ (x^2+1)^3=(x^2)^3+3\cdot(x^2)^2\cdot1+3x^2\cdot1^2+1^3=x^6+3x^4\cdot1+3x^2\cdot1+1=\\\\=x^6+3x^4+3x^2+1\\\\\\b)\ \ (x^5+x^3)^3=(x^5)^3+3\cdot(x^5)^2 \cdot x^3+3x^5\cdot(x^3)^2+(x^3)^3=\\\\=x^1^5+3x^1^0\cdot x^3+3x^5\cdot x^6+x^9=x^{15}+3x^{13}+3x^1^1+x^9[/tex]
[tex]c)\ \ (x^6-x^2)^3=(x^6)^3-3\cdot(x^6)^2\cdot x^2+3x^6\cdot(x^2)^2-(x^2)^3=\\\\=x^{18}-3x^{12}\cdot x^2+3x^6\cdot x^4-x^6=x^{18}-3x^{14}+3x^{10}-x^6\\\\\\d)\ \ (x^1^0+x^9)^3=(x^1^0)^3+3\cdot(x^1^0)^2\cdot x^9+3x^{10}\cdot(x^9)^2+(x^9)^3=\\\\=x^{30}+3x^{20}\cdot x^9+3x^{10}\cdot x^{18}+x^{27}=x^{30}+3x^{29}+3x^{28}+x^{27}[/tex]
[tex]e)\ \ (x^{33}-x^{66})^3=(x^{33})^3-3\cdot(x^{33})^2\cdot x^{66}+3x^{33}\cdot(x^6^6)^2-(x^{66})^3=\\\\=x^{99}-3x^{66}\cdot x^{66}+3x^{33}\cdot x^{132}-x^{198}\\\\\\f)\ \ (x^{100}-x^{10})^3=(x^{100})^3-3\cdot(x^{100})^2\cdot x^{10}+3x^{100}\cdot(x^{10})^2-(x^{10})^3=\\\\=x^{300}-3x^{200}\cdot x^{10}+3x^{100}\cdot x^{20}-x^{30}=x^{300}-3x^{210}+3x^{120}-x^{30}[/tex]
[tex]Zastosowane\ \ wzory\\\\(a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\(a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex]
