Variance of a 3-Asset Portfolio

What is the variance of a portfolio with 3 assets, A, B and C, with weights x_A , x_B , and x_C ?

x_Aσ_A^2 + x_Bσ_B^2 + x_Cσ_C^2 + 2x_Ax_B\mathrm{Cov}(r_A, r_B) + 2x_Ax_C\mathrm{Cov}(r_A, r_C) + 2x_Bx_C\mathrm{Cov}(r_B, r_C)

x_A^2σ_A^2 + x_B^2σ_B^2 + x_C^2σ_C^2 + 2x_Ax_B\mathrm{Cov}(r_A, r_B) + 2x_Ax_C\mathrm{Cov}(r_A, r_C) + 2x_Bx_C\mathrm{Cov}(r_B, r_C)

{\tiny x_A^2σ_A^2 + x_B^2σ_B^2 + x_C^2σ_C^2 + 2x_Ax_B\mathrm{Cov}(r_A, r_B) + 2x_Ax_C\mathrm{Cov}(r_A, r_C) + 2x_Bx_C\mathrm{Cov}(r_B, r_C) + 8x_Ax_Bx_C\mathrm{Cov}(r_A, r_B)\mathrm{Cov}(r_B, r_C)\mathrm{Cov}(r_A, r_C)}

{1 + x_A^2σ_A^2 + x_B^2σ_B^2 + x_C^2σ_C^2 + x_Ax_B\mathrm{Cov}(r_A, r_B) + x_Ax_C\mathrm{Cov}(r_A, r_C) + x_Bx_C\mathrm{Cov}(r_B, r_C)}

SOLUTION:

x_A^2σ_A^2 + x_B^2σ_B^2 + x_C^2σ_C^2 + 2x_Ax_B\mathrm{Cov}(r_A, r_B) + 2x_Ax_C\mathrm{Cov}(r_A, r_C) + 2x_Bx_C\mathrm{Cov}(r_B, r_C)

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