Factorise the polynomial $14 (3 y - 5 z)^{3} + 7 (3 y - 5 z)^{2}$

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Solution

We have
$14 (3 y - 5 z)^{3} + 7 (3 y - 5 z)^{2}$
$= 7 (3 y - 5 z)^{2} [2 (3 y - 5 z) + 1]$ [Taking $7 (3 y - 5 z)^{2}$ as common ]
$= 7 (3 y - 5 z)^{2} [6 y - 10 z + 1]$
$= 7 (3 y - 5 z) (3 y - 5 z) (6 y - 10 z + 1)$

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