Verified answer

[tex]\displaystyle\bf\\1)\\\\(a^{2} +2)^{2} =(a^{2} )^{2} +2\cdot a^{2} \cdot 2+2^{2} =a^{4} +4a^{2} +4\\\\2)\\\\(2b^{3} -4)^{2} =(2b^{3} )^{2} -2\cdot 2b^{3} \cdot 4+4^{2}=4b^{6} -16b^{3} +16\\\\3)\\\\(-2x-x^{2} )^{2} =(-2x)^{2} -2\cdot(-2x)\cdot x^{2} +(x^{2} )^{2} =4x^{2} +4x^{3} +x^{4} \\\\4)\\\\(-4c-3d)^{2} =(-4c)^{2} -2\cdot(-4c)\cdot 3d+(3d)^{2} =16c^{2} +24cd+9d^{2}\\\\5)\\\\(-k-1,5)^{2} =(-k)^{2} -2\cdot (-k)\cdot 1,5+1,5^{2} =k^{2} +3k+2,25\\\\6)[/tex]

[tex]\displaystyle\bf\\(-0,5z+2)^{2} =(-0,5z)^{2} +2\cdot(-0,5z)\cdot 2+2^{2} =0,25z^{2}-2z+4[/tex]