Select the expressions that are equivalent to 9(t + 4). Multi-select Choices: (A)9(4 + t) (B)13t (C)(t + 4)9 (D)(4 + t)9

Analyze Expression: Step 1: Analyze the given expression 9(t + 4). This expression means 9 multiplied by the sum of t and 4. Rewriting it, we get 9t + 36. Compare with (A): Step 2: Compare with choice (A) 9(4 + t). Reorder the terms inside the parentheses, it becomes 9(t + 4), which is the same as the original expression. So, (A) is equivalent. Compare with (B): Step 3: Compare with choice (B) 13t. This expression represents 13 times t, which is different from 9t + 36. So, (B) is not equivalent. Compare with (C): Step 4: Compare with choice (C) (t + 4)9. By the commutative property of multiplication, (t + 4)9 is the same as 9(t + 4). So, (C) is equivalent. Compare with (D): Step 5: Compare with choice (D) (4 + t)9. Reordering the terms inside the parentheses, it becomes (t + 4)9, which is equivalent to 9(t + 4). So, (D) is equivalent.

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Algebra 2

Simplify rational expressions

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Q. Select the expressions that are equivalent to

9(t + 4)

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Multi-select Choices:

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(A)

9(4 + t)

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(B)

13t

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(C)

(t + 4)9

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(D)

(4 + t)9

Analyze Expression: Step $1$ : Analyze the given expression $9(t + 4)$ . This expression means $9$ multiplied by the sum of $t$ and $4$ . Rewriting it, we get $9t + 36$ .
Compare with (A): Step $2$ : Compare with choice (A) $9(4 + t)$ . Reorder the terms inside the parentheses, it becomes $9(t + 4)$ , which is the same as the original expression. So, (A) is equivalent.
Compare with (B): Step $3$ : Compare with choice (B) $13t$ . This expression represents $13$ times $t$ , which is different from $9t + 36$ . So, (B) is not equivalent.
Compare with (C): Step $4$ : Compare with choice (C) $(t + 4)9$ . $\newline$ By the commutative property of multiplication, $(t + 4)9$ is the same as $9(t + 4)$ . $\newline$ So, (C) is equivalent.
Compare with (D): Step $5$ : Compare with choice (D) $(4 + t)9$ . $\newline$ Reordering the terms inside the parentheses, it becomes $(t + 4)9$ , which is equivalent to $9(t + 4)$ . $\newline$ So, (D) is equivalent.