(2n%2B5)-(n%2B3)(n-2).jpeg "(n+3)(2n+5)-(n+3)(n-2)")
Factoring and Simplifying the Expression: (n+3)(2n+5)-(n+3)(n-2)
This article will guide you through the process of factoring and simplifying the expression: (n+3)(2n+5)-(n+3)(n-2)
Step 1: Identify the Common Factor
Notice that both terms in the expression have a common factor of (n+3).
Step 2: Factor Out the Common Factor
Factor out (n+3) from both terms:
(n+3)(2n+5) - (n+3)(n-2) = (n+3)[(2n+5) - (n-2)]
Step 3: Simplify the Expression Inside the Brackets
Simplify the expression inside the brackets:
(n+3)[(2n+5) - (n-2)] = (n+3)(2n + 5 - n + 2)
(n+3)(2n + 5 - n + 2) = (n+3)(n + 7)
Step 4: Final Result
Therefore, the simplified form of the expression is:
(n+3)(2n+5)-(n+3)(n-2) = (n+3)(n+7)
Conclusion
By factoring out the common factor and simplifying the expression, we successfully transformed the original complex expression into a much simpler form. This process allows for easier manipulation and understanding of the expression, making it more useful for various mathematical applications.