To solve this problem, we will use the distributive property. The distributive property states that for any numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
[tex]\[ a(b + c) = ab + ac \][/tex]
Given the expression:
[tex]\[ 5(x + 8) \][/tex]
We need to distribute the 5 to both terms inside the parentheses, which means we'll multiply 5 by [tex]\(x\)[/tex] and then 5 by 8:
1. Multiply 5 by [tex]\(x\)[/tex]:
[tex]\[ 5 \cdot x = 5x \][/tex]
2. Multiply 5 by 8:
[tex]\[ 5 \cdot 8 = 40 \][/tex]
Now, we combine these two results:
[tex]\[ 5x + 40 \][/tex]
Therefore, the expression [tex]\(5(x + 8)\)[/tex] simplified using the distributive property is:
[tex]\[ 5x + 40 \][/tex]
So, the correct answer choice is:
[tex]\[ 5x + 40 \][/tex]
