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Which equation shows the distributive property of multiplication?\newlineChoices:\newline(A) b⋅c=c⋅bb \cdot c = c \cdot b\newline(B) (b+c)⋅d=b⋅d+c⋅d(b + c) \cdot d = b \cdot d + c \cdot d\newline(C) b⋅1=bb \cdot 1 = b\newline(D) b⋅0=0b \cdot 0 = 0

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Q. Which equation shows the distributive property of multiplication?\newlineChoices:\newline(A) b⋅c=c⋅bb \cdot c = c \cdot b\newline(B) (b+c)⋅d=b⋅d+c⋅d(b + c) \cdot d = b \cdot d + c \cdot d\newline(C) b⋅1=bb \cdot 1 = b\newline(D) b⋅0=0b \cdot 0 = 0
  1. Understand Distributive Property: Understand the distributive property of multiplication. The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. The mathematical expression for this property is a×(b+c)=a×b+a×ca \times (b + c) = a \times b + a \times c.
  2. Examine Choice (A): Examine choice (A) to see if it represents the distributive property. The equation b⋅c=c⋅bb \cdot c = c \cdot b is an example of the commutative property of multiplication, which states that the order of multiplication does not affect the product. This is not the distributive property.
  3. Examine Choice (B): Examine choice (B) to see if it represents the distributive property. The equation (b+c)⋅d=b⋅d+c⋅d(b + c) \cdot d = b \cdot d + c \cdot d is an example of the distributive property, where dd is distributed over the sum of bb and cc. This matches the definition of the distributive property.
  4. Examine Choice (C): Examine choice (C) to see if it represents the distributive property. The equation b⋅1=bb \cdot 1 = b is an example of the identity property of multiplication, which states that any number multiplied by 11 is the number itself. This is not the distributive property.
  5. Examine Choice (D): Examine choice (D) to see if it represents the distributive property. The equation b⋅0=0b \cdot 0 = 0 is an example of the multiplication property of zero, which states that any number multiplied by zero is zero. This is not the distributive property.

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