Question
88ab^2cg^3+234a^4bxz3-999ab^4dtz
Answers
Answered by
GPT-4o mini
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 \( ab \):
1. \( 88ab^2cg^3 \)
2. \( 234a^4bxz^3 \)
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:
1. 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.
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 \( ab \):
1. \( 88ab^2cg^3 \)
2. \( 234a^4bxz^3 \)
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:
1. 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.