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(2x^2+7x+10)-(x^2+2x-9)

2 min read Jun 16, 2024
(2x^2+7x+10)-(x^2+2x-9)

Simplifying the Expression: (2x^2+7x+10)-(x^2+2x-9)

This article will guide you through the process of simplifying the expression (2x^2+7x+10)-(x^2+2x-9).

Understanding the Expression

The expression involves two polynomials:

  • (2x^2+7x+10): A quadratic trinomial with a leading coefficient of 2.
  • (x^2+2x-9): Another quadratic trinomial with a leading coefficient of 1.

The operation between them is subtraction.

Simplifying the Expression

  1. Distribute the negative sign: Since we are subtracting the second polynomial, we distribute the negative sign to each term inside the parentheses:

    (2x^2 + 7x + 10) - (x^2 + 2x - 9) = 2x^2 + 7x + 10 - x^2 - 2x + 9

  2. Combine like terms: Identify terms with the same variable and exponent and combine their coefficients:

    (2x^2 - x^2) + (7x - 2x) + (10 + 9) = x^2 + 5x + 19

Solution

Therefore, the simplified expression for (2x^2+7x+10)-(x^2+2x-9) is x^2 + 5x + 19.

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