Question

factorise a^3b^3-9a^2b^2+20ab
hey mate its urgent please solve this it is very urgent ​

Answer 1

$\textbf{Given:}$

$a^3b^3-9a^2b^2+20ab$

$\textbf{To find:}$

$\text{Factors of a^3b^3-9a^2b^2+20ab }$

$\textbf{Solution:}$

$\text{Consider,}$

$a^3b^3-9a^2b^2+20ab$

$=(ab)^3-9(ab)^2+20ab$

$\text{Take}\bf\;t=ab,\;we get}$

$=t^3-9t^2+20t$

$=t[t^2-9t+20]$

$=t[t^2-4t-5t+20]$

$=t[t(t-4)-5(t-4)]$

$=t(t-4)(t-5)$

$=ab(ab-4)(ab-5)$

$a^3b^3-9a^2b^2+20ab=ab(ab-4)(ab-5)$

$\textbf{Answer:}$

$\bf\,a^3b^3-9a^2b^2+20ab=ab(ab-4)(ab-5)$

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