Combine like terms: -6 - 2y² - 3 + 3y - 2y² + 4y + 6y²

Question image

Understand the Problem

The question is asking to combine like terms in the given algebraic expression, which involves grouping similar variables together and simplifying the expression accordingly.

Answer

The simplified expression is: $$ -9 + 2y^2 + 6y $$
Answer for screen readers

The simplified expression is:

$$ -9 + 2y^2 + 6y $$

Steps to Solve

  1. Group like terms

Identify and group the like terms in the expression. Here we have:

  • Constants: $-6$, $-3$
  • $y^2$ terms: $-2y^2$, $-2y^2$, $6y^2$
  • $y$ terms: $3y$, $4y$, $-y$
  1. Combine the constants

Now sum the constants:

$$ -6 - 3 = -9 $$

  1. Combine the $y^2$ terms

Next, sum the $y^2$ terms:

$$ -2y^2 - 2y^2 + 6y^2 = (6 - 2 - 2)y^2 = 2y^2 $$

  1. Combine the $y$ terms

Then sum the $y$ terms:

$$ 3y + 4y - y = (3 + 4 - 1)y = 6y $$

  1. Write the final expression

The final expression, after combining all like terms, is:

$$ -9 + 2y^2 + 6y $$

The simplified expression is:

$$ -9 + 2y^2 + 6y $$

More Information

This process of combining like terms is fundamental in algebra, allowing for simplification of expressions and easier manipulation in equations. It's crucial for solving equations and performing polynomial operations.

Tips

  • Misidentifying like terms: Ensure that the terms have the same variable and exponent.
  • Sign errors: Be cautious with negative signs when combining terms; they can often lead to incorrect totals.

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