Question

Factor this expression completely, then place the factors in the proper location on the grid.1/8 x^3 - 1/27 y^3

Answer 1

Given:

Expression is

`(1)/(8)x^3-(1)/(27)y^3`

To find:

Factor given expression.

Step-by-step explanation:

`(a^3-b^3)=(a-b)(a^2+b^2+ab)`

Solution:

We will factor as:

`\begin{gathered} =((1)/(8)x^3-(1)/(27)y^3) \\ =((1)/(2)x)^3-((1)/(3)y)^3 \\ =((x)/(2))^3-((y)/(3))^3 \end{gathered}`
`This\text{ is of the form }(a^3-b^3)=(a-b)(a^2+ab+b^2)^`

`So,\text{ we can substitute }a=(x)/(2),b=(y)/(3)\text{ to get}`
`\begin{gathered} ((x)/(2))^3-((y)/(3))^3 \\ =((x)/(2)-(y)/(3))(((x)/(2))^2+((x)/(2))((y)/(3))+((y)/(3))^2) \\ =((x)/(2)-(y)/(3))((x^2)/(4)+(xy)/(6)+(y^2)/(9)) \end{gathered}`

This is the factor for this expression.