x^2-2xy+y^2-z^2

= (x-y)^2 - z^2

= (x-y-z)(x-y+z)

5x-5y+5x-ay

xy(x+y)+yz(y+z)+xz(x+z)+2xyz

a) 

5x-5y+ax-ay = 5(x-y) +a(x-y) = (x-y)(5+a)

b) a^3 -a^2x-ay+xy = a^2(a-x) -y(a-x) = (a-x)(a^2-y)

c) xy(x+y) +yz(y+z) +xz(x+z) +2xyz = x^2.y+xy^2 +y^2.z+xz^2 +x^2.z+xz^2 +2xyz

= (x^2.y+x^2.z)+(xy^2+xz^2+2xyz)+(y^2.z+yz^2) = x^2(y+z) +x.(y+z)^2 +yz(y+z)

=(y+z)(x^2+x+yz)

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

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

2)\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(a+5\right)\)

\(a^3-a^2x-ay+xy=a^2\left(a-x\right)-y\left(a-x\right)=\left(a-x\right)\left(a^2-y\right)\)

x² - x - y² - y

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

= (x + y)(x - y - 1)

***

9x² + y² - 16z² + 6xy

= (3x + y)² - (4z)²

= (3x + y - 4z)(3x + y + 4z)

***

a³ - a²x - ay + xy

= a²(a - x) - y(a - x)

= (a - x)(a² - y)

***

2x² - 8y² + 3x + 6y

= 2(x² - 4y²) + 3(x + 2y)

= 2(x - 2y)(x + 2y) + 3(x + 2y)

= (x + 2y)(2x - 4y + 3)

***

xy(x + y) + yz(y + z) + xz(x + z) + 2xyz

= xy(x + y + z) + yz(x + y + z) + xz(x + z)

= y(x + y + z)(x + z) + xz(x + z)

= (x + z)(xy + y² + yz + xz)

= (x + z)[y(x + y) + z(x + y)]

= (x + z)(x + y)(y + z) 

chỗ nào k hiểu hỏi mình lại ớ 

\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)

\(=xy\left(x+y\right)+xyz+xz\left(x+z\right)+xyz+yz\left(y+z\right)\)

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

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

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

a) \(5x-5y+ax-ay\)

\(\Leftrightarrow\) \(\left(5x+ax\right)-\left(5y+ay\right)\)

\(\Leftrightarrow\) \(x\left(5+a\right)-y\left(5+a\right)\)

\(\Leftrightarrow\) \(\left(5+a\right)\left(x-y\right)\)

b) \(a^3-a^2x-ay+xy\)

\(\Leftrightarrow\) \(a^2\left(a-x\right)-y\left(a-x\right)\)

\(\Leftrightarrow\) \(\left(a-x\right)\left(a^2-y\right)\)

c sai chỗ yz(x+z) sửa yz(y+z)

a,  \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)\(=x^2y+xy^2+y^2z+yz^2+x^2z+xz^2+2xyz\)

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

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

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

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

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

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

b, \(2x^2+2y^2-x^2z+z-y^2z-2\)

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

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

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

c) xét giá trị riêng

\(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)

\(=xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+xyz+xyz\)

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

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

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

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

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

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

b) x³ - ax² - xy + ay
=x³ -xy - ax² +ay
=x(x²-y) - a(x²-y)
=(x-a)(x²-y)