Question

consider the following expression.
8(9y + 4)(1 + 6)
select all of the true statements below.
9y is a factor.
1 and 6 are like terms.
in (9y + 4), 9y is a constant.
(9y + 4) is written as a sum of three terms.
in 9y, 9 is a coefficient.
none of these are true.

Explanation:

Step1: Analyze "9y is a factor"

The expression is \(8(9y + 4)(1 + 6)\). Factors are \(8\), \((9y + 4)\), and \((1 + 6)\). \(9y\) is a term inside \((9y + 4)\), not a factor of the whole expression. So this is false.

Step2: Analyze "1 and 6 are like terms"

Like terms are terms with the same variable (or no variable, i.e., constants). 1 and 6 are both constants, so they are like terms. This is true.

Step3: Analyze "In \((9y + 4)\), \(9y\) is a constant"

A constant has no variable. \(9y\) has variable \(y\), so it's a variable term, not a constant. This is false.

Step4: Analyze "\((9y + 4)\) is written as a sum of three terms"

\((9y + 4)\) has two terms: \(9y\) and \(4\). So this is false.

Step5: Analyze "In \(9y\), 9 is a coefficient"

A coefficient is the number multiplied by a variable. In \(9y\), 9 is multiplied by \(y\), so 9 is the coefficient. This is true.

Step6: Analyze "None of these are true"

Since "1 and 6 are like terms" and "In \(9y\), 9 is a coefficient" are true, this is false.

Answer:

• 1 and 6 are like terms.
• In \(9y\), 9 is a coefficient.