Question

Phân tích thành nhân tử

a) x³ + y³ + z³ - 3xyz

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

c) x(x + y) - 5x - 5y

Answer 1

a)

\(x^3+y^3+z^3-3xyz\)

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

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

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

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

Answer 2

\(x^3+y^3+z^3-3xyz\)

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

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

Answer 3

xy(x+y)+yz(y+z)+xz(x+z)+2xyz 

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

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

= xy(x + y) + z(x + y + z)(y + x) 

= (x + y)(xy + zx + zy + z²) 

= (x + y)[x(y + z) + z(y + z)] 

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

Answer 4

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

Answer 5

Mấy bài này làm dài lắm

bn đăng từng bài ik

Answer 6

thoi

đợi tí 

Answer 7

b)

\(xy\left(x+y\right)+yz\left(y+z\right)+zx\left(x+z\right)\)

\(=xy\left(x+y\right)+\left[yz\left(y+z\right)+xyz\right]+\left[zx\left(z+x\right)+x+y+z\right]\)

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

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

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

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

\(=\left(x+y\right)\left[\left(xy+zx\right)+\left(zy+z^2\right)\right]\)

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

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

Answer 8

c)

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

\(=x\left(x+y\right)-5\left(x+y\right)\)

\(=\left(x-5\right)\left(x+y\right)\)

Answer 9

ruầy bn

=))