( a + b)^4 = ( a + b)^2( a + b)^2 #160; = ( a^2 + b^2 + 2ab)( a^2 + b^2 + 2ab) = a^4 + a^2b^2 + 2a^3b + a^2b^2 + b^4 + 2ab^3 + 2a^3b + 2ab^3 + 4a ...

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Inverse of a Matrix

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Question

Expand ${(a + b)}^{4}$

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Solution

${(a + b)}^{4} = {(a + b)}^{2} {(a + b)}^{2}$
$= (a^{2} + b^{2} + 2 a b) (a^{2} + b^{2} + 2 a b)$
$= a^{4} + a^{2} b^{2} + 2 a^{3} b + a^{2} b^{2} + b^{4} + 2 a b^{3} + 2 a^{3} b + 2 a b^{3} + 4 a^{2} b^{2}$
$= a^{4} + b^{4} + 4 a^{3} b + 6 a^{2} b^{2} + 4 a b^{3}$

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