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

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

a) 12x.                           b) 4xy

c) 2y(3 x 2   +   y 2 ).

d) (x + y + z)( x 2   +   y 2   + z 2  – xy – xz - yz).

1/ ( x+y)^2 -( x-y)^2 = (x+y-x+y)(x+y+x-y)

                            =4xy

2/( 3x+1)^2-(x+1)^2= (3x+1-x-1)(3x+1+x+1)

                           =2x(4x+2)

3/

\(x^3+y^3-3x^2+3x-1\\=(x^3-3x^2+3x-1)+y^3\\=(x-1)^3+y^3\\=(x-1+y)[(x-1)^2-(x-1)y+y^2]\\=(x+y-1)(x^2-2x+1-xy+y+y^2)\)

\(x^3-3x^2y+x+3xy^2-y-y^3\\=(x^3-3x^2y+3xy^2-y^3)+(x-y)\\=(x-y)^3+(x-y)\\=(x-y)[(x-y)^2+1]\\=(x-y)(x^2-2xy+y^2+1)\)

hằng đẳng thức a²-b²=(a-b)(a+b) í bạn

a) (x+y)²-(x-y)²

=(x+y)(x-y)

b)(3x+1)²-(x+1)²

=[(3x+1)+(x+1)].[(3x+1)-(x+1)]

=(3x+1+x+1)(3x+1-x-1)

a)(x+y)²-(x-y)²

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

=2y.2x=4xy

b)(3x+1)²-(x+1)²

=(3x+1-x-1)(3x+1+x+1)

=2x.(4x+2)

=4x(2x+1)

c) x³+y³+z³-3xyz

= (x+y)³- 3xy(x+y) +z³-3xyz

=(x+y+z)( x²+2xy+y²-xz-yz+z²)-3xy(x+y+z)

=(x+y+z)(x²+y²+z²-xy-xz-yz)

Phân tích đa thức sau thành nhân tử :

a) \(\left(a+b+c\right)^3-a^3-b^3-c^3\)

b) \(x^3+y^3+z^3-3xyz\)

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

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

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

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

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

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

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

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

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

•x³+y³+z³-3xyz=(x+y)³-3xy(x+y)+z³-3xyz

=(x+y+z)[(x+y)²-(x+y).z+z²]-3xy(x+y+z)

=(x+y+z)(x²+y²+z²+2xy-xz-yz) -3xy(x+y+z)

=(x+y+z)(x²+y²+z²-xy-yz-xz)

•(x²+xy)²-(y²+xy)²=[x(x+y)]²-[y(x+y)]²

=x².(x+y)²-y².(x+y)²

=(x+y)².(x²-y²)=(x+y)².(x+y).(x-y)

=(x+y)³(x-y)

•3x²-3x-36=3.(x²-x-12)

=3(x²-4x+3x-12)

=3[x(x-4)+3(x-4)]=3(x-4)(x+3)

x³+y³+z³-3xyz=(x-y)³-3xy*(x-y)+z³-3xyz

                       =((x+y)³+z³)-3xy*(x+y+z)

                       =(x+y+z)³-3z*(x+y)*(x+y+z)-3xy*(x-y-z)

                       =(x+y+z)*((x+y+z)²-3z*(x+y)-3xy)

                       =(x+y+z)*(x²+y²+z²+2xy+2xz+2yz-3xz-3yz-3xy)

                       =(x+y+z)*(x²+y²+z²-xy-xz-yz)

(x²+xy)²-(y²+xy)²=(x²+xy+y²+xy)*(x²+xy-y²-xy)=(x²+2xy+y²)*(x²-y²)=(x+y)²*(x+y)*(x-y)=(x+y)³*(x-y)

3x²-3x-36=3*(x²-x-12)