Final answer:
The expression 330abcd + 154abd is factored by finding the common factors of the numerical coefficients and the common variables. The greatest common factor is 22, along with the common variable term abd. Thus, the factored form is 22abd(15c + 7).
Step-by-step explanation:
To factor the expression 330abcd + 154abd, we need to find the greatest common factor (GCF) of the coefficients 330 and 154 and also include any common variables. First, let's find the GCF of the numerical coefficients. The factors of 330 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, and 330. The factors of 154 are 1, 2, 7, 11, 14, 22, 77, and 154. The common factors are 1, 2, 11, and 22. The largest of these is 22.
Next, look at the variables. Both terms have abd, so we can factor abd out as well.
now, factoring out the GCF of 22 and the common variables abd, we have:
22abd(15c + 7)
This is the factored form of the given expression.