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Clear parentheses by applying the distributive property:

[tex]\[ 3(-3n + 7) - 8(6p - 9q) \][/tex]

A. [tex]\(-9n + 7 - 48p - 9q\)[/tex]

B. [tex]\(-9n + 7 - 48p + 9q\)[/tex]

C. [tex]\(-9n + 21 - 48p - 72q\)[/tex]

D. [tex]\(-9n + 21 - 48p + 72q\)[/tex]

Sagot :

GinnyAnsweridn
Let's solve the expression [tex]\(3(-3 n + 7) - 8(6 p - 9 q)\)[/tex] step-by-step by applying the distributive property.

First, distribute the constants 3 and -8 inside their respective parentheses.

### Step 1: Distribute 3 in [tex]\(3(-3 n + 7)\)[/tex]

- [tex]\(3 \cdot -3n = -9n\)[/tex]
- [tex]\(3 \cdot 7 = 21\)[/tex]

So, [tex]\(3(-3n + 7)\)[/tex] simplifies to [tex]\(-9n + 21\)[/tex].

### Step 2: Distribute -8 in [tex]\(-8(6 p - 9 q)\)[/tex]

- [tex]\(-8 \cdot 6p = -48p\)[/tex]
- [tex]\(-8 \cdot -9q = 72q\)[/tex]

So, [tex]\(-8(6p - 9q)\)[/tex] simplifies to [tex]\(-48p + 72q\)[/tex].

### Step 3: Combine the results from Step 1 and Step 2

Now we combine [tex]\(-9n + 21\)[/tex] and [tex]\(-48p + 72q\)[/tex]:

[tex]\[ 3(-3n + 7) - 8(6p - 9q) = (-9n + 21) + (-48p + 72q) \][/tex]

This simplifies to:

[tex]\[ -9n + 21 - 48p + 72q \][/tex]

Therefore, the correct answer from the given options is:

[tex]\[ \boxed{-9n + 21 - 48p + 72q} \][/tex]

Which corresponds to:

Option 4) [tex]\(-9 n + 21 - 48 p + 72 q\)[/tex]
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