5g(3g+7g^2-9) A. 50g^4-45g B. 15g^2+35g^3-45g C. 8g^2+12g^3-4g D. 8g+7g^2-9 E. 5g^4

To solve the expression $5g(3g+7g^{2}-9)$, we need to distribute the $5g$ to each term inside the parentheses.<br /><br />$5g(3g+7g^{2}-9) = 5g \cdot 3g + 5g \cdot 7g^{2} - 5g \cdot 9$<br /><br />Simplifying each term, we get:<br /><br />$5g \cdot 3g = 15g^{2}$<br /><br />$5g \cdot 7g^{2} = 35g^{3}$<br /><br />$5g \cdot 9 = 45g$<br /><br />Putting it all together, we have:<br /><br />$5g(3g+7g^{2}-9) = 15g^{2} + 35g^{3} - 45g$<br /><br />Therefore, the correct answer is B. $15g^{2}+35g^{3}-45g$.