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(x^6+10x^5-6x^2-5x)+(-9x^5+5x^3+9x^2+x+10)

2 min read Jun 17, 2024
(x^6+10x^5-6x^2-5x)+(-9x^5+5x^3+9x^2+x+10)

Simplifying Polynomial Expressions

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 most compact form.

Let's consider the following expression:

(x^6 + 10x^5 - 6x^2 - 5x) + (-9x^5 + 5x^3 + 9x^2 + x + 10)

To simplify this expression, we will follow these steps:

  1. Identify like terms: Like terms are terms that have the same variable and exponent. In our expression, we have:

    • x^6: This term is only present once.
    • x^5: We have 10x^5 and -9x^5.
    • x^3: We have 5x^3.
    • x^2: We have -6x^2 and 9x^2.
    • x: We have -5x and x.
    • Constant: We have 10.

  2. Combine like terms: We add or subtract the coefficients of the like terms.

    • x^6: Remains as x^6.
    • x^5: 10x^5 - 9x^5 = x^5
    • x^3: Remains as 5x^3.
    • x^2: -6x^2 + 9x^2 = 3x^2.
    • x: -5x + x = -4x.
    • Constant: Remains as 10.

  3. Write the simplified expression: Putting it all together, we get the simplified form:

x^6 + x^5 + 5x^3 + 3x^2 - 4x + 10

Therefore, the simplified form of the given expression is x^6 + x^5 + 5x^3 + 3x^2 - 4x + 10.

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