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Question 2 (Multiple Choice Worth 2 points)

(Equivalent Linear Expressions LC)

Which expression is equivalent to [tex]$-4(b-8)$[/tex]?

A. [tex]$-4b + 32$[/tex]

B. [tex][tex]$-4b - 32$[/tex][/tex]

C. [tex]$4b + 8$[/tex]

D. [tex]$-4b - 8$[/tex]

Sagot :

GinnyAnsweridn
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]
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