Sure, let's go through the process of simplifying the expression using the distributive property step by step:
1. Identify the Distributive Property: The distributive property states that [tex]\( a(b + c + d) = ab + ac + ad \)[/tex].
2. Apply the Distributive Property: Here, we have the expression [tex]\( 7(x - y + 3) \)[/tex]. We will distribute the '7' to each term inside the parentheses.
[tex]\[ 7(x - y + 3) = 7 \cdot x + 7 \cdot (-y) + 7 \cdot 3 \][/tex]
3. Multiply Each Term:
- [tex]\( 7 \cdot x = 7x \)[/tex]
- [tex]\( 7 \cdot (-y) = -7y \)[/tex]
- [tex]\( 7 \cdot 3 = 21 \)[/tex]
4. Combine the Results: Now, combine all the terms together.
[tex]\[ 7(x - y + 3) = 7x - 7y + 21 \][/tex]
Therefore, the simplified form of the equation is:
[tex]\[ 7(x - y + 3) = 7x - 7y + 21 \][/tex]
So, the final answer is: [tex]\( 7x \)[/tex] in the place of [tex]\( ? \)[/tex], [tex]\(-7y \)[/tex] in the place of the first [tex]\(\square\)[/tex], and [tex]\( 21 \)[/tex] in the place of the second [tex]\(\square\)[/tex].
