To solve the expression [tex]\(-4(b - 8)\)[/tex] and find an equivalent expression, let's go through the steps step-by-step using the distributive property of multiplication over subtraction.
The original expression is:
[tex]\[ -4(b - 8) \][/tex]
1. Apply the Distributive Property: This property states that [tex]\( a(b + c) = ab + ac \)[/tex]. In our case, [tex]\( a = -4 \)[/tex], [tex]\( b = b \)[/tex], and [tex]\( c = -8 \)[/tex].
2. Distribute [tex]\(-4\)[/tex] to both terms inside the parentheses:
- First term: [tex]\(-4 \times b = -4b\)[/tex]
- Second term: [tex]\(-4 \times (-8)\)[/tex]
3. Simplify the second term:
- [tex]\(-4 \times (-8) = 32\)[/tex]
4. Combine the results:
[tex]\[ -4b + 32 \][/tex]
Thus, the equivalent expression to [tex]\(-4(b - 8)\)[/tex] is:
[tex]\[ -4b + 32 \][/tex]
So, the correct choice from the given options is:
[tex]\[ -4b + 32 \][/tex]
