help w a prob.. please help

[Guest]

can u please help me solve these...........x^3-6ax^2-12a^2x-8a^3
also
x^6-y^6

(a+b)^3-1
(x-y^2 -z^2

a^4-4a^2b^2c^2 +4b^4c^4


m struggling
thanx alot

 

[soroban]

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: .\(\displaystyle (a^2\,-\,2b^2c^2)(a^2\,-\,2b^2c^2)\:=\a^2\,-\,2b^2c^2)^2\)