Answer:
I can help you find g(x+a)-g(x) for the given function. Here are the steps and the results:
- To find g(x+a)-g(x), we need to substitute x+a for x in the function g(x) and then subtract g(x) from it. Using the formula from , we can write:
g(x+a) - g(x) = (4(x+a)^2 - 5(x+a)) - (4x^2 - 5x)
- To simplify this expression, we need to expand the brackets, combine like terms, and cancel out any terms that have opposite signs. Using the rules from [this website], we can write:
g(x+a) - g(x) = (4x^2 + 8ax + 4a^2 - 5x - 5a) - (4x^2 - 5x)
g(x+a) - g(x) = 4x^2 + 8ax + 4a^2 - 5x - 5a - 4x^2 + 5x
g(x+a) - g(x) = 8ax + 4a^2 - 5a
- Therefore, g(x+a)-g(x) = 8ax + 4a^2 - 5a . This is the answer to the problem. I hope this helps you understand how to find g(x+a)-g(x) for a given function. If you have any questions, please let me know.