Ta có:  x⁶ -y⁶= (x³)²  -(y³)²  = (x³  - y³)(x³ + y³)

\(x^6-y^6\)

\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)

\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)

hk 

tốt

\(x^5+x^4+1\)

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

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

\(=x^3.\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^3-x+1\right)\)

cảm ơn bạn nhiều, không biết còn cách không? Mong nhận đượ giúp đỡ!

\(a^4+a^2+1=a^4-a^3+a^2+\left(a^3+1\right)\)

\(=a^2\left(a^2-a+1\right)+\left(a+1\right)\left(a^2-a+1\right)\)

\(=\left(a^2-a+1\right)\left(a^2+a+1\right)\)

Cách 2 lun: 

\(a^4+a^2+1=\left(a^4+2a^2+1\right)-a^2\)

\(=\left(a^2+1\right)^2-a^2=\left(a^2+a+1\right)\left(a^2-a+1\right)\)

= (a-y)² - 4²

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

\(\left(x+1\right)^4+\left(x^2+x+1\right)^2\)

\(=2x^4+6x^3+9x^2+6x+2\)(bạn nhân phá ngoặc rồi thu gọn nhé)

\(=\left(2x^4+2x^3+x^2\right)+\left(4x^3+4x^2+2x\right)+\left(4x^2+4x+2\right)\)

\(=x^2\left(2x^2+2x+1\right)+2x\left(2x^2+2x+1\right)+2\left(2x^2+2x+1\right)\)

\(=\left(x^2+2x+2\right)\left(2x^2+2x+1\right)\)

bạn ơi hình như sai đề thì phải a bạn mình nghĩ phải là \(\left(x^2-x+2\right)^2\)

\(\left(x^2-x+2\right)+\left(x-2\right)^2=\left(x^2-x+2\right)+x^2-2^2\)

\(=x^2-x+2+x^2-2^2\)\(=\left(x^2+x^2\right)+\left(2-2^2\right)-x\)

\(=2x^2-\left(2-4\right)-x=2x^2-\left(-2\right)-x\)

\(=2x^2+2-x=2x^2+2.1-x=2\left(x^2+1\right)-x\)

Lời giải:

1. 
$x^3+3x^2-16x-48=(x^3+3x^2)-(16x+48)=x^2(x+3)-16(x+3)$

$=(x+3)(x^2-16)=(x+3)(x-4)(x+4)$

2.

$4x(x-3y)+12y(3y-x)=4x(x-3y)-12y(x-3y)=(x-3y)(4x-12y)=4(x-3y)(x-3y)=4(x-3y)^2$

3.

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

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