SSC CHSL 6 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

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Question : 63 of 100

Marks: +1, -0

Simplify the following expression

(2 a-b-3 c)(4 a^{2}+b^{2}+9 c^{2}+2 a b

+6 a c-3 b c)

$-8 a^{3}+b^{3}+27 c^{3}$
$8 a^{3}+b^{3}+27 c^{3}$
$8 a^{3}-b^{3}-27 c^{3}-18 a b c$
$8 a^{3}-b^{3}-27 c^{3}+18 a b c$

Solution:

Given expression,

(2 a-b-3 c)(4 a^{2}+b^{2}+9 c^{2}+2 a b

+6 a c-3 b c)

We know that,

x^{3}+y^{3}+z^{3}-3 x y z=(x+y+z)

(x^{2}+y^{2}+z^{2}-x y-y z-z x)

∴

On comparison,

x=2 a, y=-b \;\text " and "\; z=-3 c

∴ (2 a-b-3 c)(4 a^{2}+b^{2}+9 c^{2}

\;\; +2 a b+6 a c-3 b c)

=[(2 a)^{3}+(-b)^{3}+(-3 c)^{3}-3

\;\; ×(2 a) ×(-b) ×(-3 c)]

=8 a^{3}-b^{3}-27 c^{3}-18 a b c

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