SSC CGL Tier II 21 Sep 2014 Paper

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Question : 21 of 100

Marks: +1, -0

The factors of

(a^{2}+4 b^{2}+4 b-4 a b-2 a-8 )

are

$(a-2 b-4)(a-2 b+2)$
$(a – b + 2) (a – 4b – 4)$
$(a + 2b – 4) (a + 2b + 2)$
$(a + 2b – 1) (a – 2b + 1)$

Solution:

(1)

a^{2}+4 b^{2}+4 b-4 a b-2 a-8

=a^{2}+4 b^{2}-4 a b-2 a+4 b-8

=(a-2 b)^{2}-2(a-2 b)-8

Let

(a-2 b)=x

∴

Expression

=x^{2}-2 x-8

=x^{2}-4 x+2 x-8

=x(x-4)+2(x-4)

=(x-4)(x+2)

=(a-2 b-4)(a-2 b+2)

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