The product of something means multiplying the terms together.
(2x+3) (4x^2-5x+6)
Secondly you need to distribute the terms to each other (Think of problems like FOIL)
2x 4x^2 + 2x(-5x) + 2x 6 + 3 4x^2 + 3(-5x) + 3 6
Then you must take into account that some of the numbers are negative. (minus-plus rules!)
2x 4x^2 - 2x 5x + 2x 6 + 3 4x^2 - 3 5x + 3 6
Now is the tricky part of simplifying everything.
2x 4x^2 = 8x^3
2x 5x = 10x^2
2x 6 = 12x
3 4x^2 = 12x^2
3 5x = 15x
3 6 = 18
8x^3 - 10x^2 + 12x + 12x^2 - 15x + 18
Then you group like terms.
8x^3 - 10x^2 + 12x^2 - 3x + 18
8x^2 + 2x^2 - 3x + 18
The trickiest part of this is distributing all of the terms within the parentheses, once you've done that, it's smooth sailing!
