Prove x-4 2x 2x 2x x-4 2x 2x 2x x-4-5x-44-x2-

Given: #10; #10; | x+4 amp; 2x amp; 2x #160;2x amp; x+4 amp; 2x #160;2x amp; 2x amp; x+4 | #10; #10;Use operati ...

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Determinant

Prove x+4 ...

Question

Prove $∣ ∣ ∣ ∣ \begin{matrix} x + 4 & 2 x & 2 x 2 x & x + 4 & 2 x 2 x & 2 x & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = (5 x + 4) (4 - x)^{2}$ .

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det ∣ ∣ ∣ ∣ \begin{matrix} x + 4 & 2 x & 2 x 2 x & x + 4 & 2 x 2 x & 2 x & x + 4 \end{matrix} ∣ ∣ ∣ ∣

= (5 x + 4) (4 - x)^{2}

∣ ∣ ∣ ∣ \begin{matrix} x + 4 & 2 x & 2 x 2 x & x + 4 & 2 x 2 x & 2 x & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = (5 x + 4) (4 - x)^{2}

∣ ∣ ∣ ∣ \begin{matrix} x + 4 & 2 x & 2 x 2 x & x + 4 & 2 x 2 x & 2 x & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = (5 x + 4) (4 - {x)}^{2}

∣ ∣ ∣ ∣ \begin{matrix} y + k & y & y y & y + k & y y & y & y + k \end{matrix} ∣ ∣ ∣ ∣ = k^{2} (3 y + k)

∣ ∣ ∣ ∣ \begin{matrix} x - 4 & 2 x & 2 x 2 x & x - 4 & 2 x 2 x & 2 x & x - 4 \end{matrix} ∣ ∣ ∣ ∣ = (A + B x) {(x - A)}^{2}

∣ ∣ ∣ ∣ \begin{matrix} x - 4 & 2 x & 2 x 2 x & x - 4 & 2 x 2 x & 2 x & x - 4 \end{matrix} ∣ ∣ ∣ ∣ = (A + B x) (x - A)^{2}

(A, B)

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