Combine like terms: 2y² - 5 + 1 + 2y² - 6y² - 3 - 4y.
Understand the Problem
The question is asking to combine like terms in the given algebraic expression, which includes terms with the same variable raised to the same power.
Answer
The simplified expression is $-2y^2 - 4y - 7$.
Answer for screen readers
The simplified expression is:
$$ -2y^2 - 4y - 7 $$
Steps to Solve
- Identify and Group Like Terms
Look for terms with the same variable and degree. In the expression $2y^2 - 5 + 1 + 2y^2 - 6y^2 - 3 - 4y$, group the like terms together:
- Terms with $y^2$: $2y^2 + 2y^2 - 6y^2$
- Constant terms: $-5 + 1 - 3$
- Terms with $y$: $-4y$
- Combine the $y^2$ Terms
Add the coefficients of the $y^2$ terms:
$$ 2 + 2 - 6 = -2 $$
So, the combined $y^2$ term is $-2y^2$.
- Combine the Constant Terms
Add the constant terms together:
$$ -5 + 1 - 3 = -7 $$
- Combine the $y$ Terms
The expression only has one $y$ term:
$$ -4y $$
- Write the Final Expression
Combine all the results:
$$ -2y^2 - 4y - 7 $$
The simplified expression is:
$$ -2y^2 - 4y - 7 $$
More Information
Combining like terms is a basic algebraic skill that allows you to simplify expressions for easier calculations. Remembering to group and combine similar terms ensures you perform operations accurately.
Tips
- Forgetting to include all like terms can lead to incorrect final expressions. Always ensure that each type of term is accounted for.
- Misadding numbers can occur; double-check arithmetic calculations especially with sign changes.
