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Select the expressions that are equivalent to $7(d + 4)$ . $\newline$ Multi-select Choices: $\newline$ (A) $(4 + d)7$ $\newline$ (B) $28d + 7$ $\newline$ (C) $(d + 4)7$ $\newline$ (D) $7d + 28$

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Multiplication with rational exponents

Full solution

Q. Select the expressions that are equivalent to

7(d + 4)

.

\newline

Multi-select Choices:

\newline

(A)

(4 + d)7

\newline

(B)

28d + 7

\newline

(C)

(d + 4)7

\newline

(D)

7d + 28

Distribute $7$ : Step $1$ : Distribute $7$ to each term inside the parentheses. $\newline$ Calculation: $7(d + 4) = 7d + 7\times4 = 7d + 28$
Compare with choices: Step $2$ : Compare the result with the given choices. $\newline$ Calculation: $7d + 28$ matches with choice (D)
Check other choices: Step $3$ : Check other choices for equivalence. $\newline$ Calculation: $\newline$ (A) $(4 + d)7 = 7d + 28$ (after rearranging $d$ and $4$ , multiplication is commutative) $\newline$ (C) $(d + 4)7 = 7d + 28$ (same as original expression) $\newline$ (B) $28d + 7$ does not match $7d + 28$

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