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

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

\(=\left(x^2-y^2\right)\left(y-z\right)-\left(y^2-z^2\right)\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y\right)\left(y-z\right)-\left(y-z\right)\left(y+z\right)\left(x-y\right)\)

\(=\left(x-y\right)\left(y-z\right)\left(x+y-y-z\right)\)

\(=\left(x-y\right)\left(y-z\right)\left(x-z\right)\)

B = (x + 3)(x - 1)(x - 5)(x + 15) + 64x²

B = x⁴ + 12x³ - 58x² - 180x + 225 + 64x²

B = x⁴ + 12x³ + 6x² - 180x + 225

A=(x+y)\(^3\)+z\(^3\)+3(x+y)z(x+y+z)-x\(^3\)-y\(^3\)-z\(^3\)                                                                                                    

   =x\(^3\)+y\(^3\)+3xy(x+y)+3(x+y)z(x+y+z)-x\(^3\)-y\(^3\)

   =3(x+y)(xy+zx+zy+z\(^2\))

    =3(x+y)\([\)x(y+z)+z(y+z)\(]\)

    =3(x+y)(y+z)(x+z)

  (bạn chỉ cần dùng hằng đẳng thức là ok ngay)

(x² + x + 2)(x² + 9x + 18) - 28

= x⁴ + 10x³ + 29x² + 36x + 36 - 28

= x⁴ + 10x³ + 29x² + 36x + 8 

\(a,14x^2y-21xy^2+28x^2y^2=7xy\left(x-3y+4xy\right)\\ b,x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\\ c,10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=\left(x-y\right)\left(10x+8\right)=2\left(x-y\right)\left(5x+4\right)\)

\(d,\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\)\(e,x^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)+3xyz-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)

         \(x^4+6x^3+11x^2+6x+1\)

\(=\left(x^4+6x^3+9x^2\right)+2\left(x^2+3x\right)+1\)

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

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

Chúc bạn học tốt.

a,    \(\left(x+2\right)\left(x+3\right)\left(x-7\right)\left(x-8\right)\)

\(=\left[\left(x+2\right)\left(x-7\right)\right].\left[\left(x+3\right)\left(x-8\right)\right]\)

\(=\left(x^2-5x-14\right)\left(x^2-5x-24\right)-144\)(1)

Đặt \(x^2-5x-14=t\) thì \(x^2-5x-24=t-10\)

Thay vào (1), ta có: 

     \(\left(x+2\right)\left(x+3\right)\left(x-7\right)\left(x-8\right)\) 

\(=t\left(t-10\right)-144\)

\(=t^2-10t-144\)

\(=t^2-18t+8t-144\)

\(=t\left(t-18\right)+8\left(t-18\right)\)

\(=\left(t+8\right)\left(t-18\right)\)

\(=\left(x^2-5x-14+8\right)\left(x^2-5x-14-18\right)\)

\(=\left(x^2-5x-6\right)\left(x^2-5x-32\right)\)

\(=\left(x+1\right)\left(x-6\right)\left(x^2-5x-32\right)\)

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

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

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

\(=\left[\left(x-1\right)-\left(y+1\right)\right]\left[\left(x-1\right)+\left(y+1\right)\right]\)

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

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

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

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

A. Ta có: (x - y)² - 2(x - y)+1 = (x - y)² - 2.(x - y).1 +1² = ( x - y - 1)²

B. Ta có: x² - 2y -1 - 2x +1 -y² = (x² - y²) - (2x - 2y) -1+1 = (x - y)(x + y) - 2(x - y) = (x - y)(x + y - 2)

C. Ta có: x² - y² -2y -1 = x² -(y² - 2y -1) = x² - ( y² +2y1 + 1) = x² - (y+1)² = (x - y - 1)(x + y +1) 

k cho mình nha bạn hihj!!! ~3~

a

Ta có

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

b

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

\(\left[\left(1-x\right)-y\left(1-x\right)\right]\left[\left(1+x\right)+y\left(1+x\right)\right]=\left(1-x\right)\left(1-y\right)\left(1+x\right)\left(1+y\right)\)