Multiply \[ \begin{array}{l}(x-5)\left(x^{2}-2 x+6\right) \\ (x-5)\left(x^{2}-2 x+6\right)=\square\end{array} \]

To multiply the expression \((x-5)\left(x^{2}-2x+6\right)\), we'll use the distributive property, also known as the FOIL method when applicable. Start by distributing \(x-5\) to each term in the polynomial \(x^2 - 2x + 6\): 1. Multiply \(x\) by each term in \(x^2 - 2x + 6\): \[ x \cdot x^2 = x^3 \] \[ x \cdot (-2x) = -2x^2 \] \[ x \cdot 6 = 6x \] 2. Now multiply \(-5\) by each term in \(x^2 - 2x + 6\): \[ -5 \cdot x^2 = -5x^2 \] \[ -5 \cdot (-2x) = 10x \] \[ -5 \cdot 6 = -30 \] Now, combine all these results: \[ x^3 + (-2x^2) + 6x - 5x^2 + 10x - 30 \] Combine the like terms: - For \(x^2\) terms: \(-2x^2 - 5x^2 = -7x^2\) - For \(x\) terms: \(6x + 10x = 16x\) Putting it all together, we get: \[ x^3 - 7x^2 + 16x - 30 \] Thus, the expression can be written as: \[ (x-5)(x^2-2x+6) = x^3 - 7x^2 + 16x - 30 \]