%2B(10-3x%5E2-x%2Bx%5E3).jpeg "(3x^3-7-9x^2)+(10-3x^2-x+x^3)")
Simplifying Polynomial Expressions
In mathematics, a polynomial expression is an expression consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. Simplifying polynomial expressions often involves combining like terms.
Let's simplify the given expression: (3x^3-7-9x^2)+(10-3x^2-x+x^3)
Step 1: Remove the parentheses.
Since the expression is adding two groups of terms, we can simply remove the parentheses:
3x^3 - 7 - 9x^2 + 10 - 3x^2 - x + x^3
Step 2: Identify like terms.
Like terms are terms that have the same variable and the same exponent.
- x^3 terms: 3x^3 + x^3
- x^2 terms: -9x^2 - 3x^2
- x terms: -x
- Constant terms: -7 + 10
Step 3: Combine like terms.
Combine the coefficients of the like terms:
(3 + 1)x^3 + (-9 - 3)x^2 - x + (-7 + 10)
Step 4: Simplify the expression.
4x^3 - 12x^2 - x + 3
Therefore, the simplified form of the expression (3x^3-7-9x^2)+(10-3x^2-x+x^3) is 4x^3 - 12x^2 - x + 3.