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Which equation shows the distributive property of multiplication?\newlineChoices:\newline(A) g⋅h−g⋅j=g⋅(h−j)g \cdot h - g \cdot j = g \cdot (h - j)\newline(B) g=g⋅1g = g \cdot 1\newline(C) h⋅g=g⋅hh \cdot g = g \cdot h\newline(D) g⋅h=h⋅gg \cdot h = h \cdot g

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Q. Which equation shows the distributive property of multiplication?\newlineChoices:\newline(A) g⋅h−g⋅j=g⋅(h−j)g \cdot h - g \cdot j = g \cdot (h - j)\newline(B) g=g⋅1g = g \cdot 1\newline(C) h⋅g=g⋅hh \cdot g = g \cdot h\newline(D) g⋅h=h⋅gg \cdot h = h \cdot g
  1. Identify Property: Identify 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. Mathematically, it is expressed as a(b+c)=ab+aca(b + c) = ab + ac.
  2. Examine Choice (A): Examine choice (A) to see if it matches the distributive property. Choice (A) is g⋅h−g⋅j=g⋅(h−j)g \cdot h - g \cdot j = g \cdot (h - j). This can be rewritten as g(h)−g(j)=g(h−j)g(h) - g(j) = g(h - j), which matches the form of the distributive property a(b+c)=ab+aca(b + c) = ab + ac, if we consider subtraction as adding a negative.
  3. Examine Choices (B-D): Examine choices (B), (C), and (D) to confirm they do not represent the distributive property.\newlineChoice (B) is g=g⋅1g = g \cdot 1, which represents the identity property of multiplication.\newlineChoice (C) is h⋅g=g⋅hh \cdot g = g \cdot h, and choice (D) is g⋅h=h⋅gg \cdot h = h \cdot g, both of which represent the commutative property of multiplication.\newlineNone of these choices match the form of the distributive property.

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