Sure, let's factor the given expression step-by-step:
Given expression: [tex]\( 56k^2 + 48k \)[/tex]
1. Identify the common factors:
- First, we look for the greatest common factor (GCF) between the coefficients 56 and 48.
- The GCF of 56 and 48 is 8.
- Notice [tex]\(k\)[/tex] is a common factor in both terms [tex]\( 56k^2 \)[/tex] and [tex]\( 48k \)[/tex].
2. Factor out the common factors:
- We factor out the GCF (which is [tex]\( 8 \)[/tex]) and the common variable [tex]\( k \)[/tex]:
[tex]\[
56k^2 + 48k = 8k(7k) + 8k(6)
\][/tex]
3. Simplify the factored expression:
- Combine the factors:
[tex]\[
56k^2 + 48k = 8k(7k + 6)
\][/tex]
So, the factored form is: [tex]\( 8k(7k + 6) \)[/tex].
4. Verify with the given options:
- A. [tex]\( 8 k(7 k + 6) \)[/tex]
- B. [tex]\( 24 k(7 k + 6) \)[/tex]
- C. [tex]\( 8 k(3 k + 7) \)[/tex]
- D. [tex]\( 8 k(56 k^2 + 48 k) \)[/tex]
Comparing our derived factored form with the options provided, we see that the correct choice is:
A. [tex]\( 8 k(7 k + 6) \)[/tex]
Thus, the correct answer is:
A. [tex]\( 8 k(7 k + 6) \)[/tex].
