Answer::
[tex]7m^2n^2(2m^6n^3-1)[/tex]
Explanation:
Given the expression:
[tex]14m^8n^5-7m^2n^2[/tex]
7m²n² is a common factor of the two terms.
Factor it out by dividing each of the terms to get the remainders:
[tex]14m^8n^5-7m^2n^2=7m^2n^2\mleft(\frac{14m^8n^5}{7m^2n^2}-\frac{7m^2n^2}{7m^2n^2}\mright)[/tex]
This then gives:
[tex]\begin{gathered} =7m^2n^2\mleft(\frac{7\times2\times m^2\times m^6\times n^2\times n^3}{7m^2n^2}-\frac{7m^2n^2}{7m^2n^2}\mright) \\ =7m^2n^2(\frac{7m^2n^2\times2\times m^6\times n^3}{7m^2n^2}-1) \\ =7m^2n^2(2m^6n^3-1) \end{gathered}[/tex]
The factored form of the expression is:
[tex]7m^2n^2(2m^6n^3-1)[/tex]
