Question

(x^2 - 2y^2)^3 = ? *please have a short explanation*

Answer 1

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We are aware of the identity that

$(a - b)³ = a³ - 3 {a}^{2} b + 3a {b}^{2} - b³$

So

${( {x}^{2} - 2 {y}^{2} ) }^{3}$

$= { \: ({x}^{2} )}^{3} - 3 { ({x}^{2}) }^{2} \times 2 {y}^{2} + 3 {x}^{2} {(2 {y}^{2} \: )}^{2} - { \: ({2y}^{2} )}^{3}$

$= {x}^{6} - 6 {x}^{4} {y}^{2} + 12 {x}^{2} {y}^{4} - 8 {y}^{6}$

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