Factorize $(a^2-b^2-c^2) ^2-4b^2c^2$.

Given: Polynomial: $(a^2-b^2-c^2)^2-4b^2c^2$.

To do: To factorize $(a^2-b^2-c^2)^2-4b^2c^2$.

Solution:

$(a^2-b^2-c^2)^2-4b^2c^2$

$=(a^2-b^2-c^2)^2-(2bc)^2$

$=(a^2-b^2-c^2-2bc)(a^2-b^2-c^2+2bc)$

$=(a^2-(b^2+c^2+2bc))(a^2-( b^2-2bc+c^2))$

$=(a^2-(b+c)^2)(a^2-(b-c)^2)$

$=[(a-(b+c))(a+(b+c))][(a-(b-c))(a+(b-c))]$

$=(a-b-c)(a+b+c)(a-b+c)(a+b-c)$

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Updated on: 10-Oct-2022

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