(a+b)^3 (a b)^3 =(a+b a+b)[(a+b)^2+(a+b)(a b)+(a b)^2] #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #1 ...

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Polynomial and Its General Form

a+b 3 - a-b ...

Question

${(a + b)}^{3} - {(a - b)}^{3}$

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Solution

$(a + b)^{3} - (a - b)^{3}$
$= (a + b - a + b) [(a + b)^{2} + (a + b) (a - b) + (a - b)^{2}]$ $[∵ x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2}]$
$= 2 b (a^{2} + 2 b a + b^{2} + a^{2} - b^{2} + a^{2} - 2 b a + b^{2})$
$= 2 b (3 a^{2} + b^{2})$ Ans

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