(2x%2B1)%2B3(x-1)(x%2B2)(2x%2B1).jpeg "(x-1)(2x+1)+3(x-1)(x+2)(2x+1)")
Factoring and Simplifying the Expression (x-1)(2x+1)+3(x-1)(x+2)(2x+1)
This article will guide you through factoring and simplifying the expression: (x-1)(2x+1) + 3(x-1)(x+2)(2x+1). We'll break it down step-by-step to make the process clear and understandable.
Step 1: Identify the Common Factor
The first step is to identify the common factor in the expression. Observe that both terms have (x-1)(2x+1) as a common factor.
Step 2: Factor out the Common Factor
Now, we can factor out the common factor from both terms: (x-1)(2x+1) + 3(x-1)(x+2)(2x+1) = (x-1)(2x+1)[1 + 3(x+2)]
Step 3: Simplify the Expression
Finally, we simplify the expression within the brackets: (x-1)(2x+1)[1 + 3(x+2)] = (x-1)(2x+1)(1 + 3x + 6) = (x-1)(2x+1)(3x+7)
Final Result
Therefore, the factored and simplified form of the expression is: (x-1)(2x+1) + 3(x-1)(x+2)(2x+1) = (x-1)(2x+1)(3x+7)
By following these steps, you can confidently factor and simplify similar expressions. Remember to always look for common factors and then simplify the expression to its simplest form.