How do I expand (2x+5)(9x-2)?

First, remember that a set of closed brackets directly beside a single term/another set indicates that they are being multiplied. The key to expansions like this is to do it a particular order every time to ensure that you have expanded fully. I like to use the first term in the first bracket as the starting point.
Multiply the first term in the first bracket by the first term in the second bracket.2x X 9x = 18x²Then multiply the first term in the first bracket by the second term in the second bracket. Remember to consider whether a term is positive or negative!2x X (-2) = -4x
Now we move on to the second term in the first bracket. Multiply the second term in the first bracket by the first term in the second bracket. 5 X 9x = 45xThen multiply the second term in the the first bracket by the second term in the second bracket.5 X (-2) = -10
List all of these terms and combine and like terms (bold) for your final answer:18x² - 4x +45x -10≡ 18x² +41x -10