Please expand the following brackets: (x+3)(x+5). Give your answer in its simplest form.

So how I would start to solve this problem is by using a method called the claw method (because it looks like a claw).So in order to expand the brackets, we need to multiply each term in the first bracket by each term in the second bracket. We can draw lines to show which terms are multiplying with which to keep track of which ones we have done.
Focusing on the "x" term in the first bracket, we can drawn a line to the "x" in the second bracket (this gives x squared) and then the "5" in the second bracket (this gives 5x). Next we do the same with the "3" term in the first bracket giving us 3x and 15 respectively.
The final step is to add and simplify the terms. We have x^2 + 5x + 3x + 15. By combining the like terms, the final answer is therefore x^2 + 8x + 15.