Factorise the following by grouping the terms:2p(a^2 - 2b^2) -14p… - Vidyadip

Question

Factorise the following by grouping the terms:$2p(a^2 - 2b^2) -14p + (a^2 - 2b^2)^2 - 7(a^2 - 2b^2)$

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Answer

$2p(a^2 - 2b^2) - 14p + (a^2 - 2b^2)^2 - 7(a^2 - 2b^2)$
$= 2p(a^2 - 2b^2) + (a^2 - 2b^2)^2 - 14p - 7(a^2 - 2b^2)$
$= [2p(a^2 - 2b^2) + (a^2 - 2b^2)^2] - [14p + 7(a^2 - 2b^2)]$
$= (a^2 - 2b^2)(2p + a^2 - 2b^2) - 7(2p + a^2 - 2b^2)$
$= (2p + a^2 - 2b^2)(a^2 - 2b^2 - 7).$

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