(x%2B4)-(2x-1)(3x%2B1).jpeg "(2x-1)(x+4)-(2x-1)(3x+1)")
Factoring and Simplifying Expressions: (2x-1)(x+4)-(2x-1)(3x+1)
This article will guide you through the process of factoring and simplifying the algebraic expression: (2x-1)(x+4)-(2x-1)(3x+1)
Step 1: Identifying the Common Factor
Observe that the expression contains a common factor of (2x-1) in both terms.
Step 2: Factoring out the Common Factor
We can factor out (2x-1) from both terms:
(2x-1)(x+4) - (2x-1)(3x+1) = (2x-1)[(x+4) - (3x+1)]
Step 3: Simplifying the Expression Inside the Bracket
Now, simplify the expression inside the bracket:
(2x-1)[(x+4) - (3x+1)] = (2x-1)(-2x + 3)
Step 4: Final Simplified Form
The simplified form of the expression is:
(2x-1)(-2x + 3)
This can also be written as:
(-2x + 3)(2x-1)
Conclusion
By factoring out the common factor and simplifying the expression, we obtained the simplified form (-2x + 3)(2x-1). This process demonstrates the importance of identifying common factors in algebraic expressions for simplification and further manipulation.