Hello,CARIRAMOS!
can u please help me solve these? . I think you mean "factor".
x^3 - 6ax^2 - 12a^2x - 8a^3 . Is there a typo?
You are expected to know these forms:
Difference of Squares:
.\(\displaystyle A^2\,-B^2\:=\
A\,-\,B)(A\,+\,B)\)
. . . . . Sum of Cubes:
.\(\displaystyle A^3\,+\,B^3\:=\
A\,+\,B)(A^2\,-\,AB\,+\,B^2)\)
.Difference of Cubes:
.\(\displaystyle A^3\,-\,B^3\:=\
A\,-\,B)(A^2\,+\,AB\,+\,B^2)\)
\(\displaystyle x^6\,-\,y^6\)
We have:
.\(\displaystyle (x^3)^2\,-\,(y^3)^2\:=\
x^3\,-\,y^3)(x^3\,+\,y^3)\)
. . . . . \(\displaystyle =\
x\,-\,y)(x^2\,+\,xy\,+\,y^2)(x\,+\,y)(x^2\,-\,xy\,+\,y^2)\)
\(\displaystyle (a\,+\,b)^3\,-\,1\)
Difference of Cubes:
.\(\displaystyle (a\,+\,b\\,-\,1)([a\,+\,b]^2\,+\,(a\,+\,b)\,+\,1]\)
\(\displaystyle (x-y)^2\,-\,z^2\)
Difference of Squares:
.\(\displaystyle (x\,-\,y\,-\,z)(x\,-\,y\,+\,z)\)
\(\displaystyle a^4\,-\,4a^2b^2c^2\,+\,4b^4c^4\)
Perfect square:
.\(\displaystyle (a^2\,-\,2b^2c^2)(a^2\,-\,2b^2c^2)\:=\
a^2\,-\,2b^2c^2)^2\)
