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(x+y)³-(x-y) ³-6y(x²-y²) |
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Answer» Answer: x+y) −(x−y) 3 −6y(x 2 −y 2 ) \begin{GATHERED} \TT = {(x + y)}^{3} - {(x - y)}^{3} - 3 \times 2y \times (x + y)(x - y) \\ \\ \tt = {[(x + y)}^{3} - {(x - y)]}^{3} - 3(x + y) - (x - y) \\ \tt(x + y)(x - y) \\ \\ \tt = {(x + y)}^{3} - {(x - y)}^{3} - 3(x + y)(x - y)[(x + y) - (x - y)] \\ \\ \tt = {a}^{3} - {b}^{3} - 3ab\end{gathered} =(x+y) 3 −(x−y) 3 −3×2y×(x+y)(x−y) =[(x+y) 3 −(x−y)] 3 −3(x+y)−(x−y) (x+y)(x−y) =(x+y) 3 −(x−y) 3 −3(x+y)(x−y)[(x+y)−(x−y)] =a 3 −b 3 −3ab
_______________________________________ \sf\pink{Where\:a=x+y\:and\:b=x-y}Wherea=x+yandb=x−y \begin{gathered} \sf = {(a - b)}^{3} = [(x + y) - (x - y)] {}^{3} \\ \\ \sf \leadsto \: {(2y)}^{3} = 8 {y}^{3} \end{gathered} =(a−b) 3 =[(x+y)−(x−y)] 3
⇝(2y) 3 =8y 3
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