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Question

det∣ ∣x+42x2x2xx+42x2x2xx+4∣ ∣
=(5x+4)(4x)2

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Solution

det∣ ∣x+42x2x2xx+42x2x2xx+4∣ ∣

=(x+4)det(x+42x2xx+4)2xdet(2x2x2xx+4)+2xdet(2xx+42x2x)

det(x+42x2xx+4)=3x2+8x+16

det(2x2x2xx+4)=2x2+8x

det(2xx+42x2x)=2x28x

=(x+4)(3x2+8x+16)2x(2x2+8x)+2x(2x28x)

=5x336x2+48x+64

=5x340x2+4x2+80x32x+64

=(5x+4)(16+x28x)

=(5x+4)(4x)2

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