a) 16a^2- (x-y)^2

= (4a)^2- (x-y)^2

= (4a- x +y)(4a+x-y)

b) x^3- 3x^2+ 3x-1- 27y^3

= (x^3-1)- 3x(x-1)- (3y)^3

=(x-1)(x^2+x+1)- 3x(x-1)- (3y)^3

= (x-1)(x^2+x+1-3x)- (3y)^3

= (x-1)(x^2- 2x+ 1)- (3y)^3

= (x-1)(x-1)^2- (3y)^3

= (x-1)^3- (3y)^3

= (x-1-3y)[(x-1)^2+ 3y(x-1)+ (3y)^2]

=(x-3y-1)(x^2+ 9y^2+ 3xy- 2x- 3y+1)

c)Chắc là đề bài sai phải sửa là -1 mới được

81x^4- 1

= (9x^2)^2- 1^2

= ( 9x^2-1)(9x^2+1)

d) x^10+ x^5+1

= x^10- x+ x^5- x^2+ x^2+ x+ 1

= x.(x^9-1) + x^2( x^3-1) + (x^2+x+1)

= x(x^3+1)(x^3-1)+ x^2(x^3-1)+ (x^2+x+1)

= x(x^3+1)(x-1)(x^2+x+1)+ x^2(x-1)(x^2+x+1)+ (x^2+x+1)

= [x(x^3+1)(x-1)+ x^2(x-1)+1]. (x^2+x+1)

= (x^2+ x+ 1). [x (x^4+ x- x^3-1)+ (x^3-x^2)+1]

= (x^2+ x+1)(x^5- x^4+ x^3-x+1)

d) x^8+ x^4+ 1

= x^8+ 2x^4+1 +x^4

= (x^4+1)^2+ (x^2)^2

= (x^4+1+x^2)(x^4+1-x^2)

= (x^4- x^2+1) (x^4- 2x^2+ 1+ x^2)

= (x^4- x^2+1) [(x^2-1)^2+ x^2]

= (x^4- x^2+ 1)(x^2-1+x)(x^2-1-x)