Question

which expressions are equivalent to 8(3 · 7)? select all that apply. a} 3(8 · 7) b} 3(8 + 7) c} 3(8) + 3(7) d} 8(21)

Explanation:

Step1: Simplify the given expression

First, calculate $8(3\cdot7)$. Since $3\cdot7 = 21$, then $8(3\cdot7)=8\times21 = 168$.

Step2: Analyze option a

Calculate $3(8\cdot7)$. Since $8\cdot7 = 56$, then $3(8\cdot7)=3\times56 = 168$.

Step3: Analyze option b

Calculate $3(8 + 7)$. Using the order of operations, $8+7=15$, then $3(8 + 7)=3\times15 = 45$.

Step4: Analyze option c

Calculate $3(8)+3(7)$. Using the distributive property, $3(8)+3(7)=24 + 21=45$.

Step5: Analyze option d

We already saw in Step 1 that $8(21)=168$.

Answer:

A. $3(8\cdot7)$
D. $8(21)$