y^6-z^6 help

Question

algebra 2

Answer 1

y⁶ - z⁶

 

Since this is not an equation (it's not set equal to anyhting), we can't solve for y or z - all we can do is simplify and/or factor.  Let a = y² and b = z².  The above equation then becomes:

 

a³ - b³

 

which is "difference of cubes."  There is a standard factoring formula for the difference of two cubes (google "difference of cubes").  The formula is:

 

a³ - b³ = (a - b)(a² + ab + b²)

 

Plugging a=y² and b=z² back in, we get:

 

y⁶ - z⁶ = (y² - z²)(y⁴ + y²z² + z⁴)

Answer 2

(y^3)^2- (z^3)^2

 

(y^3-z^3)(y^3+z^3)

 

(y-z)(y^2+z^2+yz)(y+z)(y^2+z^2-yz)