Question

formula for a-b the whole cube [(a-b)^3]

Answer 1

$\large\bf → (a-b)^3 = a^3 - b^3 - 3ab(a-b)$

$\bf{\underline{Derivation\:of\: formula:-}}$

$\sf (a-b)^3 = (a-b) ( a- b)^2$

$\sf ( a-b)^3 = (a-b) ( a^2 +b^2 - 2ab)$

$\sf ( a-b)^3 = a^3 + ab^2-2a^2b-a^2b-b^3+2ab$

$\sf ( a-b)^3 = a^3 - b^3 - 3a^2b + 3ab^2$

$\bf (a-b)^3 = a^3-b^3-3ab(a-b)$

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★ SOME OTHER FORMULAE ★

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

$\sf ( a-b )^2 = a^2 + b^2 - 2ab$

$\sf a^2 - b^2 = ( a+ b ) ( a-b)$

$\sf ( x + a ) ( x + b ) = x^2 + (a+b) + x + ab$

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

$\sf (a-b-c)^2 = a^2 + b^2 +c^2 - 2ab + 2bc - 2ca$

$\sf (a+b)^3 = a^3 + 3a^2b + 3ab^2+b^3$

$\sf a^3 + b^3 = (a+b) (a^2 - ab + b^2)$

$\sf a^3 - b^3 = ( a-b ) ( a^2 + ab + b^2)$