Respuesta :
Given:
Expression is
[tex]\frac{1}{8}x^3-\frac{1}{27}y^3[/tex]To find:
Factor given expression.
Explanation:
[tex](a^3-b^3)=(a-b)(a^2+b^2+ab)[/tex]Solution:
We will factor as:
[tex]\begin{gathered} =(\frac{1}{8}x^3-\frac{1}{27}y^3) \\ =(\frac{1}{2}x)^3-(\frac{1}{3}y)^3 \\ =(\frac{x}{2})^3-(\frac{y}{3})^3 \end{gathered}[/tex][tex]This\text{ is of the form }(a^3-b^3)=(a-b)(a^2+ab+b^2)^[/tex][tex]So,\text{ we can substitute }a=\frac{x}{2},b=\frac{y}{3}\text{ to get}[/tex][tex]\begin{gathered} (\frac{x}{2})^3-(\frac{y}{3})^3 \\ =(\frac{x}{2}-\frac{y}{3})((\frac{x}{2})^2+(\frac{x}{2})(\frac{y}{3})+(\frac{y}{3})^2) \\ =(\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9}) \end{gathered}[/tex]
This is the factor for this expression.
