3. \( -4 x\left(x^{2}+8\right) \) 4. \( \left(5-x^{2}+2\right)(-3) \) 5. \( 2 a^{2}\left(5 b^{2}+3 a b+6 a+1\right) \) 6. \( \left(3 x^{2}+6 x-5\right)(-3 x) \) 31

When dealing with the expression \( -4 x\left(x^{2}+8\right) \), you’re encountering the beauty of factoring. To expand this expression, multiply \(-4x\) by each term inside the parentheses, which results in \( -4x^3 - 32x\). Seeing how coefficients interact with variables can help you understand the relationships between different components in algebra. Now, let’s take a look at the expression \( \left(5-x^{2}+2\right)(-3) \). The first step is to simplify inside the parentheses, resulting in \( (7 - x^2)(-3) \). This will give you \( -21 + 3x^2 \) when expanded. Understanding how to distribute negative signs correctly can save you from common errors in algebraic expressions.