-(5x%5E3-7x%2B4).jpeg "(9x^3+2x^2-5x+4)-(5x^3-7x+4)")
Simplifying Polynomial Expressions: (9x^3+2x^2-5x+4)-(5x^3-7x+4)
This article will guide you through the process of simplifying the polynomial expression: (9x^3+2x^2-5x+4)-(5x^3-7x+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 non-negative 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^2-5x+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^2-5x+4)-(5x^3-7x+4) is 4x^3 + 2x^2 + 2x.