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A5 i) `(x-y^2)^2*(x-y^2)^(2k) = (x-y^2)^(2k+2)` `= ((x-y^2)^2)^(k+1) = (x^2-2xy^2+y^4)^(k+1)` A5 j) `(u^2sqrt(v))^(2n)*(sqrt(uv))^(2n)` `= u^(4n)v^n*u^nv^n = u^(5n)*v^(2n)= (u^5*v^2)^n` oder `(u^2sqrt(v))^(2n)*(sqrt(uv))^(2n)` `= (u^2*sqrt(v)*sqrt(uv))^(2n) = (u^2*v*sqrt(u))^(2n)` `= u^(4n)*v^(2n)*u^n = ... ` A5 k) `((2a^2b)^5)/(a^5b^5) = (2^5a^10b^5)/(a^5b^5)= 32 a^(10-5)b^(5-5) = 32a^5 b^0 = 32a^5 = (2a)^5 ` A6 a) `3x^3+5x^2 = x^2*(3x+5)` A6 b) `3x^3+5x^2+5+3x` (ist nicht zerlegbar) A6 c) `x^6y^2+2x^4y^3+x^2y^4 = x^2y^2*(x^4+2x^2y+y^2)` `= x^2y^2*(x^2+y)^2` A7 a) `(a^3b-ab^4)/(a^3b^2-a^2b^4) = (ab*(a^2-b^3) )/(a^2b^2*(a-b^2))` `= (a^2-b^3)/(ab*(a-b^2))` A7 b) `(x^7y^2-xy^8)/(x^6y-x^3y^4)= (xy^2(x^6-y^6))/(x^3y(x^3-y^3))` `=(y(x^3+y^3)(x^3-y^3))/(x^2(x^3-y^3)) ` `= (y(x^3+y^3))/x^2` |