If y=2 x+1, then what is the value of (8 x^{3}-y^{3}+6 x y) ?

SSC CGL 24 Aug 2021 Shift 2 Paper

Question : 69 of 100

Marks: +1, -0

y=2 x+1

, then what is the value of

(8 x^{3}-y^{3}+6 x y) ?

Solution:

Given,

y=2 x+1

2 x-y=-1

Cube on both sides,

(2 x-y)^{3}=(-1)^{3}

⇒\;8 x^{3}-y^{3}-3 × 2 x × y(2 x-y)=-1

⇒\; \;\; 8 x^{3}-y^{3}-6 x y(-1)=-1

∵ \; \;\; (a-b)^{3}=a^{3}-b^{3}-3 a b(a-b)

∴ \;8 x^{3}-y^{3}+6 x y=-1

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