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

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Simplify rational expressions

Full solution

Q. Select the expressions that are equivalent to

9(t + 4)

.

\newline

Multi-select Choices:

\newline

(A)

9(4 + t)

\newline

(B)

13t

\newline

(C)

(t + 4)9

\newline

(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.

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