(x-3)^2(2x+1)^3+(x-3)^3(2x+1)^2

2 min read Jun 17, 2024
(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.

Related Post