Combine like terms: 3 - 3x^2 + 6 + 3x + 1 + 4x + 2x.
Understand the Problem
The question is asking to combine like terms in the given algebraic expression. This involves identifying terms that have the same variable raised to the same power and summing their coefficients.
Answer
The combined expression is $-3x^2 + 9x + 10$.
Answer for screen readers
The combined expression is $-3x^2 + 9x + 10$.
Steps to Solve
-
Identify Like Terms Identify terms with the same variable and power. Here, we have:
- Constant terms: $3$, $6$, $1$
- Linear terms (in $x$): $3x$, $4x$, $2x$
- Quadratic term: $-3x^2$
-
Combine Constant Terms Add the constants together: $$ 3 + 6 + 1 = 10 $$
-
Combine Linear Terms Add the coefficients of the $x$ terms: $$ 3x + 4x + 2x = (3 + 4 + 2)x = 9x $$
-
Put it All Together Combine all the simplified terms: $$ 10 + 9x - 3x^2 $$
-
Rearrange Terms Organize the final expression in standard form (from highest degree to lowest degree): $$ -3x^2 + 9x + 10 $$
The combined expression is $-3x^2 + 9x + 10$.
More Information
Combining like terms is a fundamental skill in algebra that simplifies expressions, making them easier to work with. It is often the first step in solving equations.
Tips
- Forgetting to Combine All Terms: Ensure all like terms are included when combining.
- Incorrectly Adding Coefficients: Double-check the arithmetic when adding coefficients of like terms.
