Question

1. higher order thinking use the expressions below.

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

Explanation:

Step1: Recall like - term definition

Like terms have the same variables raised to the same powers.

Step2: Analyze each expression

For \(2y + 2x+4\), \(y
eq x\), so no like terms. For \(4 - 3p\), constant and variable are different. For \(8xy-6xy\), variables are same (\(x\) and \(y\)), so like terms. For \(14m+mn\), \(m\) and \(mn\) are different. For \(\frac{3}{4}m + 8m\), same variable \(m\), like terms. For \(5.75t+7.75t - t\), same variable \(t\), like terms.

Step3: Answer part a

Circle the expressions with like terms: \(8xy - 6xy\), \(\frac{3}{4}m+8m\), \(5.75t + 7.75t - t\).

Step4: Answer part b

Explain non - like - term expressions based on variable differences.

Answer:

a.

• For the expressions \(2y + 2x+4\), \(4 - 3p\), \(8xy-6xy\), \(14m+mn\), \(\frac{3}{4}m + 8m\), \(5.75t+7.75t - t\):
• \(2y + 2x+4\): No like - terms. \(2y\) and \(2x\) have different variables.
• \(4 - 3p\): No like - terms. \(4\) is a constant and \(-3p\) is a variable - term.
• \(8xy-6xy\): Has like terms. \(8xy\) and \(-6xy\) have the same variables \(x\) and \(y\) with the same exponents (implicitly \(x^1y^1\)).
• \(14m+mn\): No like - terms. \(14m\) has variable \(m\) and \(mn\) has variables \(m\) and \(n\).
• \(\frac{3}{4}m + 8m\): Has like terms. \(\frac{3}{4}m\) and \(8m\) have the same variable \(m\).
• \(5.75t+7.75t - t\): Has like terms. \(5.75t\), \(7.75t\) and \(-t\) have the same variable \(t\).
• We circle \(8xy - 6xy\), \(\frac{3}{4}m+8m\), \(5.75t + 7.75t - t\).

b. Expressions like \(2y + 2x+4\), \(4 - 3p\), \(14m+mn\) do not have like terms because the terms in them have different variables or combinations of variables. In \(2y+2x + 4\), \(y\) and \(x\) are different variables; in \(4 - 3p\), a constant and a single - variable term are different; in \(14m+mn\), \(m\) and \(mn\) have different variable structures.