Combining Like Terms - Pre Algebra

1. Simplify $2ab + 5ba$.

   $7ab$. Since $ba = ab$ by the commutative property, the terms are like terms.

2. Simplify $\frac{1}{2}x + \frac{1}{4}x$.

   $\frac{3}{4}x$. Add the coefficients: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.

3. Why are $3x^2y$ and $5xy^2$ not like terms?

   Their exponents differ: $x$ is squared in the first term, while $y$ is squared in the second.

4. Why can $4x + 3$ not be combined into a single term?

   $4x$ and 3 are not like terms: one has a variable and the other is a constant.

5. Simplify $0.5x + 1.25x$.

   $1.75x$. Add the coefficients: $0.5 + 1.25 = 1.75$.

6. Simplify $3x^2 + 2x - x^2 + 4x$.

   $2x^2 + 6x$. The $x^2$ terms and the $x$ terms are combined separately.

7. When like terms are combined, what happens to the variable part and its exponents?

   They stay the same; only the coefficients are added or subtracted. For example, $2x^2 + 3x^2 = 5x^2$, not $5x^4$.

8. What are like terms?

   Terms with the same variables raised to the same powers. Only their coefficients may differ.

9. Simplify $5m - 3n + 2m + 3n$.

   $7m$. The $m$ terms give $7m$, and $-3n + 3n = 0$.

10. Simplify $7x + 3 - 2x + 5$.

    $5x + 8$. Combine $7x - 2x = 5x$ and $3 + 5 = 8$.

11. Simplify $6y - y$.

    $5y$. The term $y$ has a coefficient of 1, so $6 - 1 = 5$.

12. Simplify $4a - 9a$.

    $-5a$. Subtract the coefficients: $4 - 9 = -5$.

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