%2B(2x-x%5E3-5x%5E4).jpeg "(-3x^3+4x^4+6x)+(2x-x^3-5x^4)")
Simplifying Polynomial Expressions
In mathematics, polynomials are expressions involving variables and coefficients, combined using addition, subtraction, and multiplication. One common task is simplifying polynomials, which involves combining like terms to express the polynomial in its simplest form.
Let's take a look at the example: (-3x^3 + 4x^4 + 6x) + (2x - x^3 - 5x^4)
Step 1: Identify Like Terms
- x^4 terms: 4x^4 and -5x^4
- x^3 terms: -3x^3 and -x^3
- x terms: 6x and 2x
Step 2: Combine Like Terms
- x^4 terms: 4x^4 - 5x^4 = -x^4
- x^3 terms: -3x^3 - x^3 = -4x^3
- x terms: 6x + 2x = 8x
Step 3: Write the Simplified Expression
Combining all the terms, the simplified expression is: -x^4 - 4x^3 + 8x
Therefore, the simplified form of (-3x^3 + 4x^4 + 6x) + (2x - x^3 - 5x^4) is -x^4 - 4x^3 + 8x.
Key Points:
- Like terms are terms with the same variable and exponent.
- When combining like terms, we only add or subtract the coefficients.
- Polynomials are usually written in descending order of exponents. This helps to organize the expression and makes it easier to work with.