%5E2(2x%2B1)%5E3%2B(x-3)%5E3(2x%2B1)%5E2.jpeg "(x-3)^2(2x+1)^3+(x-3)^3(2x+1)^2")
Factoring the Expression (x-3)²(2x+1)³ + (x-3)³(2x+1)²
This article will guide you through factoring the expression (x-3)²(2x+1)³ + (x-3)³(2x+1)².
Identifying Common Factors
The first step to factoring any expression is to identify common factors. In this case, we can see that both terms share the factors (x-3)² and (2x+1)².
Factoring Out Common Factors
Now, we can factor out these common factors:
(x-3)²(2x+1)³ + (x-3)³(2x+1)² = (x-3)²(2x+1)² [(2x+1) + (x-3)]
Simplifying the Expression
Simplifying the expression within the brackets, we get:
(x-3)²(2x+1)² [(2x+1) + (x-3)] = (x-3)²(2x+1)² (3x - 2)
Final Factored Form
Therefore, the factored form of the expression (x-3)²(2x+1)³ + (x-3)³(2x+1)² is (x-3)²(2x+1)² (3x - 2).
Summary
By identifying common factors and factoring them out, we successfully simplified the expression and obtained its factored form. This process can be applied to factor various algebraic expressions.