(-x^4+13x^5+6x^3)+(6x^3+5x^5+7x^4)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

In mathematics, simplifying polynomial expressions involves combining like terms and arranging them in a standard order. Let's simplify the expression: (-x^4 + 13x^5 + 6x^3) + (6x^3 + 5x^5 + 7x^4)

Step 1: Remove the parentheses.

Since we are adding the two polynomials, we can simply remove the parentheses:

-x^4 + 13x^5 + 6x^3 + 6x^3 + 5x^5 + 7x^4

Step 2: Combine like terms.

Identify terms with the same variable and exponent.

• x^5 terms: 13x^5 + 5x^5 = 18x^5
• x^4 terms: -x^4 + 7x^4 = 6x^4
• x^3 terms: 6x^3 + 6x^3 = 12x^3

Step 3: Arrange in standard form.

Write the terms in descending order of their exponents:

18x^5 + 6x^4 + 12x^3

Therefore, the simplified form of the expression (-x^4 + 13x^5 + 6x^3) + (6x^3 + 5x^5 + 7x^4) is 18x^5 + 6x^4 + 12x^3.