Use properties of operations to factor 8w + 16%0D%0A8%0D%0A𝑤%0D%0A %0D%0A+%0D%0A %0D%0A16%0D%0A using the GCF.

Answer 1

To factor the expression \(8w + 16\) using the greatest common factor (GCF), we first need to identify the GCF of the coefficients.

1. Identify the coefficients: The coefficients of the terms are 8 (from \(8w\)) and 16 (the constant term).

2. Find the GCF of 8 and 16:

   • The factors of 8 are: 1, 2, 4, 8
   • The factors of 16 are: 1, 2, 4, 8, 16
   • The greatest common factor is 8.

3. Factor out the GCF from the expression: \[ 8w + 16 = 8(w + 2) \]

Thus, the factored form of the expression \(8w + 16\) using the GCF is: \[ 8(w + 2) \]

Answer 2

Factor 18m − 24n%0D%0A18%0D%0A𝑚%0D%0A %0D%0A−%0D%0A %0D%0A24%0D%0A𝑛%0D%0A using the GCF

Answer 3

To factor the expression \(18m - 24n\) using the greatest common factor (GCF), follow these steps:

1. Identify the coefficients: The coefficients of the terms are 18 (from \(18m\)) and 24 (from \(-24n\)).

2. Find the GCF of 18 and 24:

   • The factors of 18 are: 1, 2, 3, 6, 9, 18
   • The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
   • The greatest common factor is 6.

3. Factor out the GCF from the expression: \[ 18m - 24n = 6(3m - 4n) \]

Thus, the factored form of the expression \(18m - 24n\) using the GCF is: \[ 6(3m - 4n) \]