Phân tích các đa thức sau thành nhân tử :
a) \(x^6-y^6\)
b) \(\left(x+y\right)^2-\left(x-y\right)^2\)
c) \(\left(3x+1\right)^2-\left(x+1\right)^2\)
d) \(x^2-10x=-25\)
e) \(x^2-x-y^2-y\)
f) \(x^2-2xy+y^2-z^2\)
h) \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)
g) \(3\left(x-3\right)\left(x+7\right)+\left(x-4\right)^2+48\)
j) \(x^3-x+y^3-y\)
a) \(x^6-y^6=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
b) \(\left(x+y\right)^2-\left(x-y\right)^2=\left(2y\right)\left(2x\right)\)
c) \(\left(3x+1\right)^2-\left(x+1\right)^2=4x\left(2x+1\right)\)
f) \(x^2-2xy+y^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
\(d,x^2-10x+25=\left(x-5\right)^2\)
\(e,x^2-x-y^2-y=x^2-y^2-x-y=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\)
\(h,xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)
\(=xy\left(x+y\right)+yz\left(y+z\right)+xyz+xz\left(x+z\right)+2xyz+xyz\)
\(=xy\left(x+y\right)+yz\left(y+z+x\right)+xz\left(x+z+y\right)\)
\(=xy\left(x+y\right)+z\left(x+y\right)\left(x+y+z\right)\)
\(=\left(x+y\right)\left(xy+zx+zy+z^2\right)\)
\(=\left(x+y\right)\left(x+z\right)\left(y+z\right)\)
\(g,3\left(x-3\right)\left(x+7\right)+\left(x-4\right)^2+48\)
\(=3\left(x^2+4x-21\right)+\left(x^2-8x+16\right)+48\)
\(=3x^2+12x-63+x^2-8x+64\)
\(=4x^2+4x+1=\left(2x+1\right)^2\)
\(j,x^3-x+y^3-y=x^3+y^3-x-y=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)=\left(x+y\right)\left(x^2-xy+y^2-1\right)\)
