1) 100-9x^2= (10)^2-(3x)^2=(10-3x) * (10+3x);
2) 16m^8 - 25n^4 = ( 4m^4)^2 - ( 5n^2)^2 = ( 4m^4 - 5n^2) * ( 4m^4 + 5n^2);
3) 4a^2 + 20ab + 25b^2 = ( 2a)^2+ 2*5b*2a + ( 5b)^2 = (2a + 5b)^2;
4) 49x^2y - y^3 = y * ( (7x)^2 - y^2) = y * ( (7x - y) * ( 7x+ y) ) ;
5) - 6m^2 + 12 mn - 6n^2 = -6 ( m^2 - 2mn + n^2) = -6 ( ( m-n)^2) ;
6) b^3 - 8c^3 = b^3 - ( 2c)^3 = ( b - 2c) * ( b + 2bc + 2c);