`36)`
`27 - 27m + 9m^2 - m^3`
`= - (m^3 - 9m^2 + 27m - 27)`
` = -(m^3 - 3 . m^2 . 3 + 3 . m . 3^2 - 3^3)`
`= - (m-3)^3`
`37)`
`125 - (x+2)^3`
` = 5^3 - (x+2)^3`
` = [ 5- (x+2)] . [ 5^2 + 5 (x+2) + (x+2)^2]`
`= (5 - x - 2)(25 + 5x + 10 + x^2 + 4x + 4)`
`= (3-x)(x^2 + 9x + 29)`
``
`(x+3)^3 - 8`
` = (x+3)^3 - 2^3`
` = [ (x+3) - 2 ] [ (x+3)^2 + 2 (x+3) + 2^2]`
` = (x+ 3 -2)(x^2+ 6x + 9 + 2x+6+4)`
` = (x+1)(x^2 + 8x + 19)`
`38)`
`(x+3)^3- 64`
`= (x+3)^2 - 4^3`
` = [ (x+3) - 4] . [ (x+3)^2 + 4(x+3) + 4^2]`
`= (x + 3 - 4)(x^2 + 6x+ 9 + 4x + 12 + 16)`
`= (x-1) (x^2 + 10x + 37)`
``
`(x+1)^3 - 125`
` = (x+1)^3 - 5^3`
` = [ (x+1) - 5] . [ (x+1)^2 + 5 (x+1) + 5^2]`
`= (x + 1 - 5)(x^2+ 2x + 1 + 5x + 5 + 25)`
` = (x - 4)(x^2 + 7x + 31)`
`39)`
`x^9 - 1`
` = (x^9 + x^6 + x^3)- (x^6 + x^3 + 1)`
`= x^3 (x^6 + x^3 + 1) - (x^6 + x^3 + 1)`
`= (x^3 - 1)(x^6 + x^3 + 1)`
`= (x-1)(x^2 + x +1)(x^6 + x^3 + 1)`
``
`x^9 + 1`
`=( x^9 - x^6 + x^3 )+( x^6 - x^3 + 1)`
`= x^3 (x^6 - x^3 + 1) + (x^6 - x^3 + 1)`
`= (x^3 + 1)(x^6 - x^3 + 1)`
`= (x+1)(x^2 - x+1)(x^6 - x^3+ 1)`
