Identify the GCF of 12a4b3 + 8a3b2
12a^4b^3 + 8a^3b^2 = 4a^3b^2(3ab+2).
GCF = 4a^3b^2.
To identify the greatest common factor (GCF) of the expression 12a4b3 + 8a3b2, you need to find the highest power of each variable that divides both terms without remainder.
Step 1: Factor out the numerical coefficients (12 and 8) first:
12a4b3 + 8a3b2 = 4(3a4b3) + 4(2a3b2)
Step 2: Look at the variables. Both terms have a factor of a3b2.
Step 3: The highest power of a is 4 in the first term and 3 in the second term. The highest power of b is 3 in the first term and 2 in the second term.
Step 4: To find the GCF, take the lowest power of each variable. So, the GCF of 12a4b3 + 8a3b2 is 4a3b2.