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Identify the factors of [tex]6ab - 8a + 21b - 28[/tex].

A. [tex]\((2a + 4)(3b - 7)\)[/tex]
B. [tex]\((2a - 4)(3b + 7)\)[/tex]
C. [tex]\((2a + 7)(3b - 4)\)[/tex]
D. [tex]\((2a - 7)(3b + 4)\)[/tex]

Sagot :

GinnyAnsweridn
To identify the factors of the expression [tex]\(6ab - 8a + 21b - 28\)[/tex], let's go through the factorization step by step.

First, take a look at the given expression:
[tex]\[6ab - 8a + 21b - 28\][/tex]

### Step 1: Group the terms to find common factors
We can group the terms in pairs to factor by grouping:

Group 1: [tex]\(6ab - 8a\)[/tex]
Group 2: [tex]\(21b - 28\)[/tex]

### Step 2: Factor out the greatest common factor (GCF) from each group
From the first group, [tex]\(6ab - 8a\)[/tex]:
- The GCF of [tex]\(6ab\)[/tex] and [tex]\(-8a\)[/tex] is [tex]\(2a\)[/tex].
- Factor [tex]\(2a\)[/tex] out:
[tex]\[6ab - 8a = 2a(3b - 4)\][/tex]

From the second group, [tex]\(21b - 28\)[/tex]:
- The GCF of [tex]\(21b\)[/tex] and [tex]\(-28\)[/tex] is [tex]\(7\)[/tex].
- Factor [tex]\(7\)[/tex] out:
[tex]\[21b - 28 = 7(3b - 4)\][/tex]

### Step 3: Combine the factored expressions
Now we have:
[tex]\[6ab - 8a + 21b - 28 = 2a(3b - 4) + 7(3b - 4)\][/tex]

Notice that both groups contain a common factor [tex]\((3b - 4)\)[/tex]. We can factor this out:
[tex]\[(2a + 7)(3b - 4)\][/tex]

Thus, the factors of [tex]\(6ab - 8a + 21b - 28\)[/tex] are:
[tex]\[\boxed{(2a + 7)(3b - 4)}\][/tex]

So, the correct answer is [tex]\((2a + 7)(3b - 4)\)[/tex].
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