Question

which equation shows the distributive property of multiplication?
2 = 2 × 1
0 × (8 − 7) = 0 × 8 − 0 × 7
0 × 4 0
9 × 8 = 8 × 9
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Explanation:

Step1: Recall the distributive property

The distributive property of multiplication over subtraction (or addition) states that \(a\times(b - c)=a\times b - a\times c\) (or \(a\times(b + c)=a\times b + a\times c\)).

Step2: Analyze each option

• Option 1: \(2 = 2\times1\) is just a multiplication fact showing the identity property (since \(2\times1 = 2\)), not distributive.
• Option 2: \(0\times(8 - 7)=0\times8 - 0\times7\) follows the form \(a\times(b - c)=a\times b - a\times c\) where \(a = 0\), \(b = 8\), \(c = 7\), so this is the distributive property.
• Option 3: \(0\times4 = 0\) is the zero property of multiplication (any number times 0 is 0), not distributive.
• Option 4: \(9\times8 = 8\times9\) is the commutative property of multiplication (order of multiplication doesn't matter), not distributive.

Answer:

\(0\times(8 - 7)=0\times8 - 0\times7\) (the second option)