Answered

Apply the distributive property to factor out the greatest common factor.

[tex]\[ 60m - 40 = \square \][/tex]



Answer :

Sure, I'd be happy to help you understand this problem step-by-step.

We need to factor out the greatest common factor (GCF) from the expression [tex]\(60m - 40\)[/tex].

1. Identify the GCF of 60 and 40:
- The GCF is the largest number that can evenly divide both 60 and 40.
- The factors of 60 are [tex]\(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\)[/tex].
- The factors of 40 are [tex]\(1, 2, 4, 5, 8, 10, 20, 40\)[/tex].
- The highest common factor between 60 and 40 is 20.

Therefore, the GCF of 60 and 40 is [tex]\(20\)[/tex].

2. Factor out the GCF from each term in the expression [tex]\(60m - 40\)[/tex]:
- Divide [tex]\(60m\)[/tex] by the GCF [tex]\(20\)[/tex]:
[tex]\[ \frac{60m}{20} = 3m \][/tex]
- Divide [tex]\(-40\)[/tex] by the GCF [tex]\(20\)[/tex]:
[tex]\[ \frac{-40}{20} = -2 \][/tex]

3. Rewrite the expression using the GCF and the simplified terms:
[tex]\[ 60m - 40 = 20 \cdot (3m) - 20 \cdot (2) \][/tex]

4. Combine the terms inside parentheses:
[tex]\[ 60m - 40 = 20 \cdot (3m - 2) \][/tex]

So, the factored form of the expression [tex]\(60m - 40\)[/tex] is:
[tex]\[ 20 \cdot (3m - 2) \][/tex]

Therefore, the answer is:
[tex]\[ \boxed{20 \cdot (3m - 2)} \][/tex]