Simplifying the Expression: (5x12x^2+9x^3)(5x^3+6x3)
This article will guide you through simplifying the given expression: (5x12x^2+9x^3)(5x^3+6x3).
Understanding the Basics
Before we start, let's recall some key concepts:
 Combining Like Terms: We can only add or subtract terms that have the same variable and exponent. For example, 5x and 6x are like terms, but 5x and 5x² are not.
 Distributing the Negative Sign: When we have a minus sign in front of parentheses, it means we distribute the negative sign to each term inside the parentheses.
StepbyStep Solution

Distribute the negative sign:
(5x  12x² + 9x³)  (5x³ + 6x  3) becomes 5x  12x² + 9x³  5x³  6x + 3

Rearrange the terms by their exponents:
9x³  5x³  12x² + 5x  6x + 3

Combine like terms:
(9x³  5x³) + (12x²) + (5x  6x) + 3

Simplify:
4x³  12x²  x + 3
Final Answer
The simplified expression is 4x³  12x²  x + 3.