How do you factor #x^3 - y^6#?

1 Answer
Apr 25, 2018

Answer:

#(sqrtx-y)(sqrtx+y)(x^2+xy^2+y^4)#

Explanation:

#"this can be expressed as a "color(blue)"difference of cubes"#

#•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)#

#"with "a=x" and "b=y^2to(y^2)^3=y^6#

#=(x-y^2)(x^2+xy^2+y^4)#

#"we can express "x-y^2" as a "color(blue)"difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#"with "a=sqrtx" and "b=y#

#=(sqrtx-y)(sqrtx+y)#

#rArrx^3-y^6=(sqrtx-y)(sqrtx+y)(x^2+xy^2+y^4)#