x^7+x+1

=x.x^6+x.1+x.1/x

=x.(x^6+1+1/x)

tk 

Sửa đề x^7 chuyển thành x^8

Ta có

\(x^8+x+1=x^8-x^2+x^2+x+1\)

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

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

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

\(=\left(x^2+x+1\right)\left(x^6+x^3-x^5-x^2+1\right)\)

(4x-x-y)(4x+x+y)

= (3x-y)(5x+y)

sorry phải là

(2x-x-y)(2x+x+y)

=(x-y)(3x+y)

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

\(=\left(2x-x-y\right)\left(2x+x+y\right)\)   ( dùng hằng đẳng thức hiệu 2 bình phương)

còn câu trên

giải cả hai câu ms đc k

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

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

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-3\)(1)

Đặt \(x^2+5x=t\)

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

\(=t^2+3t-t-3=t\left(t+3\right)-\left(t+3\right)\)

\(=\left(t-1\right)\left(t+3\right)\)(2)

Mà \(x^2+5x=t\)nên \(\left(2\right)=\left(x^2+5x-1\right)\left(x^2+5x+3\right)\)

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

\(x^3+y^3+z^3-3xyz=\left(x+y\right)^3-3x^2y-3xy^2+z^3-3xyz\)

\(=\left[\left(x+y\right)^3+z^3\right]-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left[\left(x+y\right)^2-z\left(x+y\right)+z^2\right]-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2-3xy\right)\)

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

=x * x * x + y * y * y + z * z * z

=

Ta có: \(x^3+y^3+z^3-3xyz=\left(x+y\right)^3+z^3-3x^2y-3xy^2-3xyz\)

\(=\left(x+y+z\right)\text{[}\left(x+y\right)^2-\left(x+y\right).z+z^2\text{]}-3xy\left(x+y+z\right)\)

\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2-3xy\right)\)

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

\(x^2-5x+6\)

\(=x^2-2x-3x+6\)

\(=x\cdot\left(x-2\right)-3\left(x-2\right)\)

\(=\left(x-2\right)\cdot\left(x-3\right)\)

\(x^2-5x+6\)

\(=x^2-2x-3x+6\)

\(=x\left(x-2\right)-3\left(x-2\right)\)

\(=\left(x-2\right).\left(x-3\right)\)

x² - 5x + 6

= x² - 2x - 3x + 6 

= x. ( x - 2 ) - 3 . ( x - 2 )

= ( x - 2 ) . ( x - 3 )

Ta có : 

\(\left|1-2x\right|-\left|3x+1\right|=0\)

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

\(\Leftrightarrow\)\(\orbr{\begin{cases}1-2x=3x+1\\1-2x=-3x-1\end{cases}\Leftrightarrow\orbr{\begin{cases}3x+2x=1-1\\-2x+3x=-1-1\end{cases}}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}5x=0\\x=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-2\end{cases}}}\)

Vậy \(x=0\) hoặc \(x=-2\)

Chúc bạn học tốt ~ 

cảm ơn Phùng Minh Quân nhiều !!!

a: \(2x^3+x^2-13x+6\)

\(=2x^3-4x^2+5x^2-10x-3x+6\)

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

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

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

b: \(2x^2+y^2-6x+2xy-2y+5=0\)

\(\Leftrightarrow x^2+2xy+y^2+x^2-4x+4-2x-2y+1=0\)

\(\Leftrightarrow\left(x+y\right)^2+\left(x-2\right)^2-2\left(x+y\right)+1=0\)

\(\Leftrightarrow\left(x-2\right)^2+\left(x+y-1\right)^2=0\)

=>x-2=0 và x+y-1=0

=>x=2 và y=-1