\( provethatthefollowingexpressionaretrueusingthedistributiveproperty(d\times (g+h)=(d\times g)+(d\times h) \)

To prove the expression \( d \times (g + h) = (d \times g) + (d \times h) \) using the distributive property, let's break it down. By definition, the distributive property states that multiplying a number by a sum is the same as multiplying each addend in the sum by that number and then adding the products together. For example, if \( d = 2 \), \( g = 3 \), and \( h = 4 \), we have: 1. Calculate the left side: \( d \times (g + h) = 2 \times (3 + 4) = 2 \times 7 = 14 \). 2. Calculate the right side: \( (d \times g) + (d \times h) = (2 \times 3) + (2 \times 4) = 6 + 8 = 14 \). Since both sides are equal, this demonstrates that \( d \times (g + h) = (d \times g) + (d \times h) \) holds true. This proof can be applied to any values of \( d \), \( g \), and \( h \), reinforcing the key idea behind the distributive property!