factor the common factor out of each expression.
1) $2mn^7 - 4$
2) $9x^2y - 2x^2$
3) $-4y^7x + 3y^5$
4) $-54y^3x - 48y^2$

Question

Accepted Answer

### Problem 1: $ 2mn^7 - 4 $
# Explanation:
## Step1: Find the GCF of coefficients and variables.
The GCF of 2 and 4 is 2. There are no common variables between $ mn^7 $ and 1 (since -4 can be thought of as $ -4 \times 1 $).
## Step2: Factor out the GCF.
$ 2mn^7 - 4 = 2(mn^7 - 2) $
# Answer: $ 2(mn^7 - 2) $

### Problem 2: $ 9x^2y - 2x^2 $
# Explanation:
## Step1: Find the GCF of coefficients and variables.
The GCF of 9 and 2 is 1 (for coefficients), but the common variable part is $ x^2 $ (since both terms have $ x^2 $).
## Step2: Factor out the common variable part.
$ 9x^2y - 2x^2 = x^2(9y - 2) $
# Answer: $ x^2(9y - 2) $

### Problem 3: $ -4y^7x + 3y^5 $
# Explanation:
## Step1: Find the GCF of coefficients and variables.
The GCF of -4 and 3 is 1 (for coefficients), and the common variable part is $ y^5 $ (since $ y^7x $ has $ y^5 $ as a factor and $ y^5 $ has $ y^5 $ as a factor).
## Step2: Factor out the common variable part.
$ -4y^7x + 3y^5 = y^5(-4y^2x + 3) $
# Answer: $ y^5(-4xy^2 + 3) $ (or $ y^5(3 - 4xy^2) $)

### Problem 4: $ -54y^3x - 48y^2 $
# Explanation:
## Step1: Find the GCF of coefficients and variables.
First, find the GCF of 54 and 48. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54; factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The GCF is 6. Also, the common variable part is $ y^2 $ (since $ y^3x $ has $ y^2 $ and $ y^2 $ has $ y^2 $). Also, we can factor out a negative sign with the GCF for simplicity (or just factor out -6$ y^2 $). Let's factor out -6$ y^2 $.
## Step2: Factor out the GCF (including the negative sign for simplicity).
$ -54y^3x - 48y^2 = -6y^2(9yx + 8) $ (or $ -6y^2(9xy + 8) $)
# Answer: $ -6y^2(9xy + 8) $

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QUESTION IMAGE

Question

Explanation:

Problem 1: \( 2mn^7 - 4 \)

Step1: Find the GCF of coefficients and variables.

Step2: Factor out the GCF.

Step1: Find the GCF of coefficients and variables.

Step2: Factor out the common variable part.

Step1: Find the GCF of coefficients and variables.

Step2: Factor out the common variable part.

Answer:

Problem 2: \( 9x^2y - 2x^2 \)