-3xy-(x-1)(x%2Bxy).jpeg "(12x^3y-12x^2y^2) 3xy-(x-1)(x+xy)")
Simplifying the Expression: (12x³y - 12x²y²) 3xy - (x-1)(x+xy)
This expression involves a combination of multiplication, subtraction, and factoring. Let's break it down step-by-step to simplify it.
Step 1: Distribute the 3xy
First, we distribute the 3xy across the first set of parentheses:
(12x³y - 12x²y²) 3xy = 36x⁴y² - 36x³y³
Step 2: Expand the Second Set of Parentheses
Next, we expand the second set of parentheses using the distributive property or the FOIL method:
(x-1)(x+xy) = x² + x²y - x - xy
Step 3: Combine the Expanded Terms
Now, let's combine the results from steps 1 and 2, remembering to subtract the entire second expression:
36x⁴y² - 36x³y³ - (x² + x²y - x - xy) = 36x⁴y² - 36x³y³ - x² - x²y + x + xy
Step 4: Rearrange and Combine Like Terms
Finally, we can rearrange the terms and combine any like terms:
36x⁴y² - 36x³y³ - x² - x²y + x + xy
This is the simplified form of the original expression.