To simplify the expression \( 88ab^2cg^3 + 234a^4bxz^3 - 999ab^4dtz \), we can look for common factors in each term.
The given expression is:
\[ 88ab^2cg^3 + 234a^4bxz^3 - 999ab^4dtz \]
Step 1: Identify common factors.
In each of the terms, we can see that there is at least one factor of \( ab \):
- \( 88ab^2cg^3 \)
- \( 234a^4bxz^3 \)
- \( -999ab^4dtz \)
Step 2: Factor out the common terms.
The common factors \( ab \) can be factored out, but we also need to consider the coefficients:
-
The coefficients are 88, 234, and -999. To factor further, we can find the greatest common divisor (GCD) of the coefficients.
- GCD(88, 234) = 2
- GCD(2, -999) = 1 (since -999 is not even)
So, we can only factor out \( ab \) and \( b \) from the terms where it is available. The minimum power of \( b \) we have is \( b^2 \) from the first term, but we cannot factor out \( b^3 \) because it appears in the last term.
Thus, we can factor out \( ab^2 \):
\[ ab^2(88c g^3 + 234a^3 xz^3 - 999bdtz) \]
Final Expression:
So the factored form of the original expression is:
\[ ab^2(88cg^3 + 234a^3 xz^3 - 999bdtz) \]
This form retains all of the information from the original expression, organized for clarity.