What is the product? \( -9 x(5-2 x) \) \( 18 x^{2}-45 x \) \( -18 x^{2}-45 x \) \( -18 x-45 x \) \( 18 x-45 x \)

The expression \( -9 x(5-2 x) \) can be simplified by distributing \( -9x \) across the terms inside the parentheses. This gives us: \[ -9x \cdot 5 + (-9x) \cdot (-2x) = -45x + 18x^2 \] Rearranging this, we find the product is: \[ 18x^2 - 45x \] So the correct choice from your options is \( 18 x^{2}-45 x \). To avoid common mistakes when distributing, remember to carefully multiply both terms inside the parentheses by the factor outside. It's like making sure you apply the right amount of seasoning to your dish—too little or too much can lead to a completely different outcome! Also, always check that you keep your variable and constant terms organized to avoid confusion later.