Question

consider the following expression.
\\(4(8 + 3)(9u + 5)\\)
select all of the true statements below.
\\(\square\\ (9u + 5)\\) is written as a sum of three terms.
\\(\square\\ 8\\) and \\(3\\) are like terms.
\\(\square\\) in \\(9u\\), \\(9\\) is a coefficient.
\\(\square\\) in \\((9u + 5)\\), \\(9u\\) is a constant.
\\(\square\\ 4\\) is a factor.
\\(\square\\) none of these are true.

Explanation:

Step1: Analyze (9u+5) term count

$(9u+5)$ has two terms: $9u$ and $5$, so the statement is false.

Step2: Check if 8 and 3 are like terms

Like terms have same variable type; 8 and 3 are constants, so this is true.

Step3: Verify 9 as coefficient in 9u

A coefficient is the number multiplying a variable; 9 multiplies $u$, so this is true.

Step4: Check if 9u is a constant

Constants have no variables; $9u$ has $u$, so the statement is false.

Step5: Confirm 4 as a factor

The expression is $4\times(8+3)\times(9u+5)$, so 4 is a factor; this is true.

Step6: Eliminate final option

Since some statements are true, this is false.

Answer:

• 8 and 3 are like terms.
• In 9u, 9 is a coefficient.
• 4 is a factor.