Question

1. higher order thinking use the expressions below. 14m + mn; -3/4m + 8m + m; 5.75t + 7.75t - t; 2y + 2x + 4; 4 - 3p; 8xy - 6xy. a. circle the expressions that have like terms. b. explain why the other expressions do not have like terms.

Explanation:

Step1: Recall the definition of like - terms

Like terms have the same variable(s) raised to the same power(s).

Step2: Analyze $\frac{-3}{4}m + 8m + m$

All terms have the variable $m$ only, so they are like terms.

Step3: Analyze $5.75t+7.75t - t$

All terms have the variable $t$ only, so they are like terms.

Step4: Analyze $8xy - 6xy$

Both terms have the variables $x$ and $y$ together, so they are like terms.

Step5: Analyze $14m+mn$

$14m$ has variable $m$ and $mn$ has variables $m$ and $n$, different variable parts.

Step6: Analyze $2y + 2x+4$

$2y$ has variable $y$, $2x$ has variable $x$, different variable parts.

Step7: Analyze $4 - 3p$

One term is a constant and the other has variable $p$, different in nature.

Answer:

a. The expressions with like - terms are: $\frac{-3}{4}m + 8m + m$, $5.75t+7.75t - t$, $8xy - 6xy$.
b. The expressions $14m+mn$, $2y + 2x+4$, $4 - 3p$ do not have like terms because:

• In $14m+mn$, the first term has only the variable $m$ and the second term has variables $m$ and $n$. Since the variable parts are different, they are not like terms.
• In $2y + 2x+4$, the first term has the variable $y$, the second term has the variable $x$, and the third term is a constant. The variable parts of the first two terms are different, so there are no like terms.
• In $4 - 3p$, the first term is a constant and the second term has the variable $p$. They are not like terms as one is a constant and the other has a variable.