Which of the expressions is a decomposition of the expression below?
18c2ab−99abc2
To solve this problem, we will follow these steps:
- Step 1: Determine the greatest common divisor (GCD) of the numeric coefficients 18 and 99.
The GCD of 18 and 99 is 9 since 18=2×9 and 99=11×9.
- Step 2: Analyze the variables in the terms 18c2ab and −99abc2.
Both terms have the fraction form with c2ab and −abc2.
- Step 3: Identify the common algebraic fraction factor.
The common factor from the algebraic component is c2ab.
- Step 4: Factor c2ab out from the expression.
The expression 18c2ab−99abc2 can be rewritten as:
9c2ab(2−11a2b2c4).
Therefore, the decomposition of the given expression is 9c2ab(2−11a2b2c4).
9c2ab(2−11a2b2c4)