\(=\left(x^2+x+4\right)^2+3x\left(x^2+x+4\right)+5x\left(x^2+x+4\right)+15x^2\\ =\left(x^2+x+4\right)\left(x^2+x+4+3x\right)+5x\left(x^2+x+4+3x\right)\\ =\left(x^2+x+4+3x\right)\left(x^2+x+4+5x\right)\\ =\left(x^2+4x+4\right)\left(x^2+6x+4\right)\\ =\left(x+2\right)^2\left(x^2+6x+4\right)\)

\(x^4-8x=x\left(x^3-8\right)=x\left(x-2\right)\left(x^2+2x+4\right)\)

x⁴ - 8x = x.(x³ - 8) = x. (x³ - 2³) = x.(x - 2).(x² + 2x +4)

`x^4 - 8x`

`= x(x^3 - 8)`

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

x⁴ - 4x³ - 8x² + 8x 

 = x(x³ - 4x² - 8x + 8) 

= x[x³ + 8 - 4x(x + 2)] 

= x[(x + 2)(x² - 2x + 4) - 4x(x + 2)] 

= x(x + 2)(x² - 6x + 4)

= x(x + 2)(x² - 6x + 9 - 5) 

 = \(x\left(x+2\right)\left[\left(x-3\right)^2-5\right]=x\left(x+2\right)\left(x-3+\sqrt{5}\right)\left(x-3-\sqrt{5}\right)\)

\(x^4-4x^3-8x^2+8x\)

\(=x\left(x^3-4x^2-8x+8\right)\)

\(=x\left(x^3-6x^2+2x^2+4x-12x+8\right)\)

\(=x\left[\left(x^3-6x^2+4x\right)+\left(2x^2-12x+8\right)\right]\)

\(=x\left[x\left(x^2-6x+4\right)+2\left(x^2-6x+4\right)\right]\)

\(=x\left(x^2-6x+4\right)\left(x+2\right)\)

\(=x\left[\left(x-3\right)^2-\left(\sqrt{5}\right)^2\right]\left(x+2\right)\)

\(=x\left(x-3-\sqrt{5}\right)\left(x-3+\sqrt{5}\right)\left(x+2\right)\)

`#3107`

`x^4 - 8x + 63`

`= x^4 + 4x^3 + 9x^2 - 4x^3 -16x^2 - 36x + 7x^2 + 28x + 63`

`= (x^4 + 4x^3 + 9x^2) - (4x^3 + 16x^2 + 36x) + (7x^2 + 28x + 63)`

`= x^2(x^2 + 4x + 9) - 4x(x^2 + 4x + 9) + 7(x^2 + 4x + 9)`

`= (x^2 + 4x + 9)(x^2 - 4x + 7)`

____

`64x^4 + y^4`

`= 64x^4 + 16x^2y^2 + y^4 - 16x^2y^2`

`= (64x^4 + 16x^2y^2 + y^4) - (16x^2y^2)`

`= [(8x^2)^2 + 2*8x^2*y^2 + (y^2)^2] - (4xy)^2`

`= (8x^2 + y^2)^2 - (4xy)^2`

`= (8x^2 + y^2 - 4xy)(8x^2 + y^2 + 4xy)`

____

`x^3 + 3xy`

`= x(x^2 + 3y)`

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

THAM KHẢO

\(x^3-x^2-4x^2+8x-4\)

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

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

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

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

\(x^3+5x^2+8x-4=x^3+x^2+4x^2+4x+4x+4\)

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

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

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

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

easy

\(\left(x^4+3\right)-8x\)

\(\sqrt{\left(x^4+3\right)}^2-\sqrt{8x}^2\)

\(\left(\sqrt{\left(x^4+3\right)}-\sqrt{8x}\right)\left(\sqrt{\left(x^4+3\right)}+\sqrt{8x}\right)\)

\(1,\\ 1,=15\left(x+y\right)\\ 2,=4\left(2x-3y\right)\\ 3,=x\left(y-1\right)\\ 4,=2x\left(2x-3\right)\\ 2,\\ 1,=\left(x+y\right)\left(2-5a\right)\\ 2,=\left(x-5\right)\left(a^2-3\right)\\ 3,=\left(a-b\right)\left(4x+6xy\right)=2x\left(2+3y\right)\left(a-b\right)\\ 4,=\left(x-1\right)\left(3x+5\right)\\ 3,\\ A=13\left(87+12+1\right)=13\cdot100=1300\\ B=\left(x-3\right)\left(2x+y\right)=\left(13-3\right)\left(26+4\right)=10\cdot30=300\\ 4,\\ 1,\Rightarrow\left(x-5\right)\left(x-2\right)=0\Rightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\\ 2,\Rightarrow\left(x-7\right)\left(x+2\right)=0\Rightarrow\left[{}\begin{matrix}x=7\\x=-2\end{matrix}\right.\\ 3,\Rightarrow\left(3x-1\right)\left(x-4\right)=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=4\end{matrix}\right.\\ 4,\Rightarrow\left(2x+3\right)\left(2x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)

\(x^3-5x^2+8x-4\)

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

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

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

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

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

Xong rùi đấy

ko cần gải mk nghĩ ra roiif

cảm ơn bạn 

a) x⁴ - y⁴

= (x²)² - (y²)²

= (x² - y²)(x² + y²)

= (x - y)(x + y)(x² + y²)

b) 1 - 8x³y⁶

= 1³ - (2xy²)³

= (1 - 2xy²)(1 + 2xy² + 4x²y⁴)