Find the Common Factor of 22abc - 11ab/c: Algebraic Expression Analysis

Question

Find the common factor:

22abc11abc 22abc-\frac{11ab}{c}

Video Solution

Step-by-Step Solution

To find the common factor for the expression 22abc11abc 22abc - \frac{11ab}{c} , we will follow these steps:

  • Step 1: Determine the common factors in terms of coefficients and variables.
  • Step 2: Factor these common elements out of the expression.
  • Step 3: Simplify the expression after factoring.

Now, let's proceed with the solution:

Step 1: Identify the common factors.
The expression is 22abc11abc 22abc - \frac{11ab}{c} . We can see that both terms have the factors 11ab 11ab . 11 is a common numerical factor in 22 and 11. Ab is also present in both terms.

Step 2: Factor out the common factors.
Factor out 11ab 11ab from each term in the expression:

22abc11abc=11ab(22abc11ab(11abc)11ab) 22abc - \frac{11ab}{c} = 11ab \left( \frac{22abc}{11ab} - \frac{\left(\frac{11ab}{c}\right)}{11ab} \right)

Step 3: Simplify the terms inside the parenthesis.

  • Simplify the first term: 22abc11ab=2c\frac{22abc}{11ab} = 2c
  • Simplify the second term: 11abc11ab=1c\frac{\frac{11ab}{c}}{11ab} = \frac{1}{c}

Thus, we get the factored form:

11ab(2c1c) 11ab\left(2c - \frac{1}{c}\right)

Therefore, the common factor form of 22abc11abc 22abc - \frac{11ab}{c} is 11ab(2c1c) 11ab(2c - \frac{1}{c}) .

Answer

11ab(2c1c) 11ab(2c-\frac{1}{c})