Question

8 cube - ( 2 x-y) cube​

Answer 1

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$\bf {8}^{3} - ( 2 x-y) ^{3}$

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$\bf {8}^{3} - ( 2 x-y) ^{3}$

$\sf = ( {2x} ) ^{3} - (2x - y)^{3}$

$\sf \: By \: using \: identity \\ \red{\boxed{(a³-b³=(a-b)(a²+ab+b²)}}$

$\sf = (y)(4 {x}^{2} + 4 {x}^{2} + {y}^{2} - 4xy + 4 {x}^{2} - 2xy)$

$\large\purple {\boxed{ \sf =y(12 {x}^{2} - 6xy + {y}^{2}) }}$

Step-by-step explanation:

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Identity I: 

$\boxed{ \sf{(a + b)^2 = a^2 + 2ab + b^2}}$

Identity II: 

$\boxed{ \sf{(a – b)^2 = a^2 – 2ab + b^2}}$

Identity III: 

$\boxed{ \sf a^2 – b^2= (a + b)(a – b)}$

Identity IV: 

$\boxed{ \bf{(x + a)(x + b) = x^2 + (a + b) x + ab}}$

Identity V: 

$\boxed{ \sf{(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca}}$

Identity VI:

 

$\boxed{ \sf{(a + b)^3 = a^3 + b^3 + 3ab (a + b)}}$

Identity VII:

 

$\boxed{ \sf{(a – b)^3 = a^3 – b^3 – 3ab (a – b)}}$

Identity VIII: 

$\boxed{ \sf{a^3 + b^3 + c^3 – 3abc = (a + b + c)(a^2 + b^2 + c^2 – ab – bc – ca)}}$