What is expand \det(2(A^t+B^t)^3) ?

The solution to expand \det(2(A^t+B^t)^3) is \det(2A^{3t}+6B^tA^{2t}+6A^tB^{2t}+2B^{3t})

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expand \det(2(A^t+B^t)^3)

expand

det (2 (A^{t} + B^{t})^{3})

det (2 A^{3 t} + 6 B^{t} A^{2 t} + 6 A^{t} B^{2 t} + 2 B^{3 t})

Solution steps

det (2 (A^{t} + B^{t})^{3})

(A^{t} + B^{t})^{3} = A^{3 t} + 3 B^{t} A^{2 t} + 3 A^{t} B^{2 t} + B^{3 t}

= det (2 (3 A^{t} B^{2 t} + A^{3 t} + 3 B^{t} A^{2 t} + B^{3 t}))

Expand

2 (A^{3 t} + 3 B^{t} A^{2 t} + 3 A^{t} B^{2 t} + B^{3 t}) : 2 A^{3 t} + 6 B^{t} A^{2 t} + 6 A^{t} B^{2 t} + 2 B^{3 t}

= det (2 A^{3 t} + 6 B^{t} A^{2 t} + 6 A^{t} B^{2 t} + 2 B^{3 t})

7 (4 + 711)

(x + 3 y) (2 x - y)

\frac{z ^{2}}{( z + 2 i ) ^{2} \cdot ( z ^{2} + 9 )}

(5 i, - 8 j) m

\frac{( 2 \cdot k + 2 ) !}{( k + 1 ) \cdot 2 ^{k + 1}}

What is expand \det(2(A^t+B^t)^3) ?
The solution to expand \det(2(A^t+B^t)^3) is \det(2A^{3t}+6B^tA^{2t}+6A^tB^{2t}+2B^{3t})