Factor 63a-45b-9c

Factor 63a-45b-9c.

The correct answer and explanation is:

The given expression is 63a−45b−9c63a – 45b – 9c. To factor this expression, the first step is to look for the greatest common factor (GCF) of all the terms.

1. Find the GCF of the coefficients:
   • The coefficients of 63a63a, 45b45b, and 9c9c are 63, 45, and 9, respectively.
   • The GCF of 63, 45, and 9 is 9.
2. Factor out the GCF:
   • Now, factor 9 out of each term:
   63a−45b−9c=9(7a−5b−c)63a – 45b – 9c = 9(7a – 5b – c)
3. Verify the factorization:
   • Distribute 9 across the terms inside the parentheses:
   9(7a−5b−c)=63a−45b−9c9(7a – 5b – c) = 63a – 45b – 9c
   • This matches the original expression, so the factorization is correct.

Thus, the factored form of 63a−45b−9c63a – 45b – 9c is: 9(7a−5b−c)9(7a – 5b – c)

In summary, factoring involves finding the greatest common factor of the terms and then factoring it out. In this case, the GCF was 9, and once we factored it out, we were left with the expression 7a−5b−c7a – 5b – c inside the parentheses. This process makes the expression easier to work with in various contexts, such as solving equations or simplifying further.