Sure, let's solve the given problem step-by-step using the distributive property.
Given the expression:
[tex]\[ 10(x + 10) \][/tex]
Step 1: Identify the parts of the expression.
Here, we have the number 10 which will be distributed over the addition inside the parentheses [tex]\( (x + 10) \)[/tex].
Step 2: Apply the distributive property.
The distributive property states that [tex]\( a(b + c) = ab + ac \)[/tex]. In our case, [tex]\( a = 10 \)[/tex], [tex]\( b = x \)[/tex], and [tex]\( c = 10 \)[/tex]. We need to multiply 10 by each term inside the parentheses separately.
Step 3: Multiply 10 by [tex]\( x \)[/tex].
[tex]\[ 10 \times x = 10x \][/tex]
Step 4: Multiply 10 by 10.
[tex]\[ 10 \times 10 = 100 \][/tex]
Step 5: Combine the results from steps 3 and 4.
[tex]\[ 10x + 100 \][/tex]
So, the expression [tex]\( 10(x + 10) \)[/tex] using the distributive property is written as:
[tex]\[ 10x + 100 \][/tex]
Therefore, the equivalent expression is:
[tex]\[ 10x + 100 \][/tex]
