Verified answer

[tex]\displaystyle\bf\\1)\\\\-4+900y^{6} =900y^{6} -4=(30y^{3} )^{2} -2^{2} =\\\\=(30y^{3} -2)\cdot(30y^{3} +2)\\\\2)\\\\1\frac{24}{25} m^{6} n^{4} -1\frac{9}{16} a^{2} b^{8} =\frac{49}{25} m^{6} n^{4} -\frac{25}{16} a^{2} b^{8} =\\\\\\=\Big(\frac{7}{5} m^{3} n^{2} \Big)^{2} -\Big(\frac{5}{4} ab^{4} \Big)^{2} =\Big(\frac{7}{5} m^{3} n^{2} -\frac{5}{4} ab^{4} \Big)\cdot\Big(\frac{7}{5} m^{3} n^{2} +\frac{5}{4} ab^{4} \Big)=[/tex]

[tex]\displaystyle\bf\\=\Big(1,4 m^{3} n^{2} -1,25ab^{4} \Big)\cdot \Big(1,4 m^{3} n^{2} +1,25ab^{4} \Big)\\\\3)\\\\49-(3c-5)^{2} =7^{2} -(3c-5)^{2} =\\\\=(7-3c+5)\cdot(7+3c-5)=(12-3c)\cdot(2+3c)=\\\\=3\cdot(4-c)\cdot(2+3c)\\\\4)\\\\(2a-5)^{2} -(a+6)^{2} =(2a-5-a-6)\cdot(2a-5+a+6)=\\\\=(a-11)\cdot(3a+1)[/tex]