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

User Chaka
by
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1 Answer

1 vote

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.

User Sslepian
by
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