a,
`16x^2-81y^4=(4x)^2-(9y^2)^2=(4x-9y^2)(4x+9y^2)`
b,
`1/25-36y^2=(1/5)^2-(6y)^2=(1/5-6y)(1/5+6y)`
c,
`4-y^6/9=2^2-(y^3/3)^2=(2-y^3/3)(2+y^3/3)`
d,
`25x^6-(4y^2)/(49)=(5x^3)^2-((2y)/7)^2=(5x^3-(2y)/7)(5x^3+(2y)/7)`
e,
`27x^3-1/8=(3x)^3-(1/2)^3=(3x-1/2)[(3x)^2+3x . 1/2+(1/2)^2]=(3x-1/2)(9x^2+3/2x+1/4)`
f,
`125x^3-1=(5x)^3-1^3=(5x-1)[(5x)^2+5x.1+1^2]=(5x-1)(25x^2+5x+1)`
g,
`8x^3+125=(2x)^3+5^3=(2x+5)[(2x)^2-2x.5+5^2]=(2x+5)(4x^2-10x+25)`