$$ provethatthefollowingexpressionaretrueusingthedistributiveproperty(d imes (g+h)=(d imes g)+(d imes h) $$

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$$ provethatthefollowingexpressionaretrueusingthedistributiveproperty(d	imes (g+h)=(d	imes g)+(d	imes h) $$

UpStudy AI · Accepted Answer

To prove that the expression $$ d \times (g + h) = (d \times g) + (d \times h) $$ is true using the distributive property, we can follow these steps:

1. **Identify the components**: 
   - Let $$ d $$ be a constant or variable.
   - Let $$ g $$ and $$ h $$ be variables.

2. **Apply the distributive property**: 
   The distributive property states that for any numbers (or variables) $$ a $$, $$ b $$, and $$ c $$:
   $$
   a \times (b + c) = (a \times b) + (a \times c)
   $$
   In our case, we can set $$ a = d $$, $$ b = g $$, and $$ c = h $$.

3. **Substitute into the property**:
   Using the values we identified:
   $$
   d \times (g + h) = (d \times g) + (d \times h)
   $$

4. **Conclusion**:
   Since we have applied the distributive property correctly, we have shown that:
   $$
   d \times (g + h) = (d \times g) + (d \times h)
   $$
   Therefore, the expression is true.

This completes the proof using the distributive property.
$$ d \times (g + h) = (d \times g) + (d \times h) $$ is true by the distributive property.

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