%2B(2x%5E3-3x%5E2-7).jpeg "(4x^3-6x^2+x)+(2x^3-3x^2-7)")
Simplifying Polynomials: A Step-by-Step Guide
In mathematics, polynomials are expressions consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. Simplifying polynomials involves combining like terms to express the polynomial in its simplest form.
Let's explore how to simplify the following polynomial expression:
(4x^3 - 6x^2 + x) + (2x^3 - 3x^2 - 7)
Step 1: Identify like terms
Like terms are terms that have the same variables raised to the same powers. In our expression, we have the following like terms:
- x^3 terms: 4x^3 and 2x^3
- x^2 terms: -6x^2 and -3x^2
- x terms: x (only one term)
- Constant terms: -7 (only one term)
Step 2: Combine like terms
To combine like terms, simply add or subtract their coefficients. Let's apply this to our expression:
- x^3 terms: 4x^3 + 2x^3 = 6x^3
- x^2 terms: -6x^2 - 3x^2 = -9x^2
- x terms: x (remains unchanged)
- Constant terms: -7 (remains unchanged)
Step 3: Write the simplified polynomial
Now that we have combined all the like terms, we can write the simplified expression:
(4x^3 - 6x^2 + x) + (2x^3 - 3x^2 - 7) = 6x^3 - 9x^2 + x - 7
Therefore, the simplified form of the given polynomial expression is 6x^3 - 9x^2 + x - 7.