c) 2y ³ + 8y ² + 8y d) x ³ – 64x e) 8a ²xy – 18b ²xy f) 32a ³b ³ – 4 g) x ² – 49z ² – 4xy + 4y ² h) 3x ² + 6x + 3 – 3y ² i) 12x ²y – 12y ³ + 36xy + 27

@Meo_

c) $2y^{3}$ + $8y^{2}$ + 8y

= 2y($y^{2}$ + 4y + 4 )

d) x ³ – 64x

= x($x^{2}$ + 64 )

e) 8a ²xy – 18b ²xy

= 2xy( 4a ² – 9b ² )

f) 32a ³b ³ – 4

= 4(8a ³b ³ – 1 )

g) x ² – 49z ² – 4xy + 4y ²

= ( x ²  – 4xy + 4y ² ) – 49z ²

= ( x – y ) ² – 49z²

= ( x – y ) ² – ( 7z )²

= ( x – y – 7z ) ( x – y + 7z )

h) 3x ² + 6x + 3 – 3y ²

= ( 3x ² + 6x + 3  ) – 3y ²

= [ 3 ( x² + 2x + 1 ) ] – 3y ²

= 3 ( x² + 2x + 1 – y ² )

i) 12x ²y – 12y ³ + 36xy + 27y

= ( 12x ²y – 12y ³ ) + ( 36xy + 27y )

= 12y( x² – y² ) + 9(4x + 3)

= 3 [ 4y( x² – y² ) + 3(4x + 3) ]