Simplify the following expression:

$-1-3 x-6+2 x^2+3 x^2-6 x$

Combine the constant terms: − 1 − 6 = − 7 .
Combine the x terms: − 3 x − 6 x = − 9 x .
Combine the x 2 terms: 2 x 2 + 3 x 2 = 5 x 2 .
Write the simplified expression in standard form: 5 x 2 − 9 x − 7 ​ .

Explanation

Understanding the Problem We are asked to simplify the expression − 1 − 3 x − 6 + 2 x 2 + 3 x 2 − 6 x . This involves combining like terms, which are terms with the same variable raised to the same power. We will combine the constant terms, the x terms, and the x 2 terms separately, and then write the simplified expression in standard form (decreasing order of exponents).

Combining Constant Terms First, let's combine the constant terms: − 1 and − 6 . − 1 − 6 = − 7

Combining x Terms Next, let's combine the x terms: − 3 x and − 6 x . − 3 x − 6 x = − 9 x

Combining x^2 Terms Now, let's combine the x 2 terms: 2 x 2 and 3 x 2 . 2 x 2 + 3 x 2 = 5 x 2

Writing the Simplified Expression Finally, we write the simplified expression in standard form (decreasing order of exponents): 5 x 2 − 9 x − 7


Examples
Simplifying algebraic expressions is a fundamental skill in mathematics with numerous real-world applications. For instance, consider a scenario where a company's profit is modeled by the expression − 1 − 3 x − 6 + 2 x 2 + 3 x 2 − 6 x , where x represents the number of units sold. Simplifying this expression to 5 x 2 − 9 x − 7 allows the company to easily analyze how their profit changes with varying sales volumes. This simplification aids in making informed business decisions, such as determining the optimal production level to maximize profit.

Answered by GinnyAnswer | 2025-07-03

The expression − 1 − 3 x − 6 + 2 x 2 + 3 x 2 − 6 x simplifies to 5 x 2 − 9 x − 7 . We combine like terms: the constants, x terms, and x^2 terms. The final result is presented in standard form.
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Answered by Anonymous | 2025-07-04