ab(a+b)+bc(b+c)+ca(c+a)+3abc

=(ab(a+b)+abc)+(bc(b+c)+abc)+(ca(c+a)+abc)

=ab(a+b+c)+bc(b+c+a)+ca(c+a+b)

=(a+b+c)(ab+bc+ca)

   a^3 + b^3 +c^3 - 3abc 

= ( a + b )^3 - 3ab ( a + b ) + c^3 - 3abc 

= [ ( a + b )^3 + c^3 ] + [ -3ab ( a + b ) - 3abc ] 

= ( a + b + c ) * [ ( a + b )^2 - c*( a + b ) + c^2 ] - 3ab ( a + b + c ) 

= ( a + b + c ) * ( a^2 + 2ab + b^2 - ac - bc + c^2 - 3ab ) 

= (a + b + c) * ( a^2 + b^2 + c^2 - ab - ac - bc )

\(=6x^2+5x-3xy\)

\(=x\left(6x+5-3y\right)\)

x⁸+64

=(x⁴)²+16x⁴+8²-16x⁴

=(x⁴+8)²-(4x²)²

=(x⁴+8-4x²)(x⁴+8+4x²)

\(x^2-4x+4-y^2\)

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

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

(x - 2)² - y² = (x - 2 - y)(x - 2 + y)

\(x^2-4x-y^2+4=\left(x-2\right)^2-y^2=\left(x-y-2\right)\left(x+y-2\right)\)

\(x^2-4x+4-y^2\)

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

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

(x - 2)² - y² = (x - 2 - y)(x - 2 + y)

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

\(=x\left(x-4\right)+5\left(x-4\right)=\left(x+5\right)\left(x-4\right)\)

x(x-4)+5(x-4)

(x+5)(x-4)