To factor the expression 48m^4n^7 + 24m^3n^5 - 36m^2n, we can look for the greatest common factor (GCF) among the terms.
Step 1: Identify the GCF of the coefficients.
The coefficients of the terms are 48, 24, and -36. The GCF of these coefficients is 12, as it is the largest number that divides evenly into all three coefficients.
Step 2: Identify the GCF of the variables.
The variables in the terms are m and n. For m, the highest power is 4 in the first term, 3 in the second term, and 2 in the third term. Therefore, the GCF of m is m^2. For n, the highest power is 7 in the first term, 5 in the second term, and 1 in the third term. Therefore, the GCF of n is n^1 or simply n.
Step 3: Factor out the GCF.
Factoring out the GCF, we get:
12m^2n(4m^2n^6 + 2mn^4 - 3)
So, the factored form of the expression 48m^4n^7 + 24m^3n^5 - 36m^2n is 12m^2n(4m^2n^6 + 2mn^4 - 3).
