Simplifying Polynomial Expressions: (9x^3+2x^25x+4)(5x^37x+4)
This article will guide you through the process of simplifying the polynomial expression: (9x^3+2x^25x+4)(5x^37x+4).
Understanding the Basics
Before we begin, let's recall some key concepts:
 Polynomials: Expressions consisting of variables and constants combined using addition, subtraction, and multiplication, with nonnegative integer exponents.
 Simplifying Polynomials: Combining like terms to write the polynomial in its most concise form.
 Like Terms: Terms that have the same variable(s) raised to the same power.
The Steps to Simplify

Distribute the negative sign: The minus sign in front of the second parenthesis means we multiply each term inside the parenthesis by 1:
(9x^3+2x^25x+4) + (1 * 5x^3) + (1 * 7x) + (1 * 4)

Simplify:
9x^3 + 2x^2  5x + 4  5x^3 + 7x  4

Combine like terms: Identify terms with the same variables and exponents, and add their coefficients:
(9x^3  5x^3) + 2x^2 + (5x + 7x) + (4  4)

Final result:
4x^3 + 2x^2 + 2x
The Simplified Expression
Therefore, the simplified form of the polynomial expression (9x^3+2x^25x+4)(5x^37x+4) is 4x^3 + 2x^2 + 2x.