To simplify the expression [tex]\(4(5x + 3y - 7)\)[/tex] using the distributive property, follow these steps:
1. Understand the Distributive Property: The distributive property states that [tex]\(a(b + c + d) = ab + ac + ad\)[/tex]. This means you need to multiply each term inside the parentheses by the number outside the parentheses.
2. Distribute the 4 to Each Term Inside the Parentheses:
- First, multiply 4 by [tex]\(5x\)[/tex].
- Second, multiply 4 by [tex]\(3y\)[/tex].
- Third, multiply 4 by [tex]\(-7\)[/tex].
3. Perform Each Multiplication:
- [tex]\(4 \cdot 5x = 20x\)[/tex]
- [tex]\(4 \cdot 3y = 12y\)[/tex]
- [tex]\(4 \cdot (-7) = -28\)[/tex]
By distributing the 4 to each term inside the parentheses, we get:
[tex]\[
4(5x + 3y - 7) = 20x + 12y - 28
\][/tex]
So, the simplified equation using the distributive property is:
[tex]\[
4(5x + 3y - 7) = 20x + 12y - 28
\][/tex]
Thus, the answer is:
[tex]\[
4(5x + 3y - 7) = 20x + 12y - 28
\][/tex]
This gives us the final values:
- Coefficient of [tex]\(x\)[/tex] is 20
- Coefficient of [tex]\(y\)[/tex] is 12
- Constant term is [tex]\(-28\)[/tex]
Therefore, in the original equation's format:
[tex]\[
4(5 x+3 y-7) = 20x + 12y - 28
\][/tex]
