`27)`
`4x^4 - 16x^2y^3 + 16y^6`
`= 4 (x^4 - 4x^2y^3 + 4y^6)`
`= 4 [ (x^2)^2 - 2 . x^2 . 2y^3 + (2y^3)^2]`
` = 4 (x^2 - 2y^3)^2`
`28)`
`9x^4 - 12x^5 + 4x^6`
`= x^4 (9 - 12x + 4x^2)`
`= x^4 [ 3^2 - 2 . 3 . 2x + (2x)^2]`
`= x^4 (3 - 2x)^2`
`29)`
`x^10 - 4x^8 + 4x^6`
`= x^6 (x^4 - 4x^2 + 4)`
` = x^6 [ (x^2) -2 . x^2 .2 + 2^2]`
`= x^6 (x^2 - 2)^2`
`30)`
`8x^6 - 27y^3`
`= (2x^2)^3 - (3y)^3`
` = (2x^2 - 3y) [ (2x^2)^2 + 2x^2 . 3y + (3y)^2]`
` = (2x^2 - 3y)(4x^4 + 6x^2y + 9y^2)`
`31)`
`(a+b)^3 - c^3`
` = [ (a+b) - c] [ (a+b)^2 + c (a+b) + c^2]`
`= ( a+b-c)(a^2 + 2ab + b^2 + ac + bc + c^2)`
`32)`
`x^3 - (y-1)^3`
` = [ x - (y-1)] [ x^2 + x (y-1) + (y-1)^2]`
` = (x - y + 1)(x^2 + xy - x + y^2 - 2y + 1)`
`33)`
`x^6 - 1`
` = (x^3)^2 - 1^2`
`= (x^3 - 1)(x^3+ 1)`
`= (x-1)(x^2 + x+1)(x-1)(x^2 - x +1)`
``
`x^6 + 1`
`= (x^6 - x^4 +x^2) + (x^4 - x^2 + 1)`
`= x^2 (x^4 - x^2 + 1) + (x^4 - x^2 + 1)`
`= (x^2+ 1)(x^4 - x^2+ 1)`
`34)`
`x^6 - y^6`
`= (x^3)^2 - (y^3)^2`
` = (x^3 - y^3)(x^3 +y^3)`
`= (x-y)(x^2 + xy + y^2)(x+y)(x^2 - xy + y^2)`
``
`x^12 - y^4`
` = (x^6)^2 - (y^2)^2`
` = (x^6 - y^2)(x^6 + y^2)`
` = [ (x^3)^2- y^2](x^6 + y^2)`
` = (x^3 - y)(x^3+y)(x^6+y^2)`
`35)`
`1/27 + a^3`
` = (1/3)^3 + a^3`
`= (1/3 + a) [ (1/3)^2 - 1/3 . a + a^2]`
` = (1/3 + a)(1/9 - 1/3a + a^2)`
``
`1/8x^3-8`
`= (1/2x)^3 - 2^3`
` = (1/2x - 3)[ (1/2x)^2 + 1/2x . 3+ 3^2]`
` = (1/2 x- 3) (1/4 x^2 + 3/2x + 9)`
`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`
