To identify the property that has been used to simplify the expression [tex]\(4(5+8) = 20 + 32\)[/tex], let's examine the steps involved in the simplification process.
1. Start with the original expression:
[tex]\[4(5+8)\][/tex]
2. Apply the property to simplify inside the parentheses:
[tex]\[4 \times (5 + 8)\][/tex]
3. Distribute the multiplication over addition:
[tex]\[4 \times 5 + 4 \times 8\][/tex]
In this step, we multiplied 4 by each term inside the parentheses, which gave us:
[tex]\[4 \times 5 + 4 \times 8 = 20 + 32\][/tex]
By examining these steps, we can see that the process involves multiplying each term inside the parentheses by the number outside the parentheses, thus distributing the factor across the terms. This is a clear use of the Distributive Property of Multiplication over Addition.
Therefore, the property that has been applied in simplifying the expression [tex]\(4(5+8) = 20 + 32\)[/tex] is:
The distributive property
