## Expanding and Simplifying the Expression: (n^2-3n+1)(2n+3)

This article will guide you through the process of expanding and simplifying the given expression: **(n^2-3n+1)(2n+3)**.

### Step 1: Expanding the Expression

We can expand the expression by applying the distributive property (also known as FOIL - First, Outer, Inner, Last):

**First:**Multiply the first terms of each binomial: n² * 2n =**2n³****Outer:**Multiply the outer terms of the binomials: n² * 3 =**3n²****Inner:**Multiply the inner terms of the binomials: -3n * 2n =**-6n²****Last:**Multiply the last terms of the binomials: -3n * 3 =**-9n**

Now, we multiply the monomial (2n + 3) by the constant term:

- 1 * 2n =
**2n** - 1 * 3 =
**3**

### Step 2: Combining Like Terms

We have the following terms after expansion:

2n³ + 3n² - 6n² - 9n + 2n + 3

Now, combine the terms with the same powers of 'n':

**2n³**- (3n² - 6n²) =
**-3n²** - (-9n + 2n) =
**-7n** **3**

### Step 3: Simplified Expression

Combining all the terms, we get the simplified expression:

**2n³ - 3n² - 7n + 3**

Therefore, the expanded and simplified form of the expression (n²-3n+1)(2n+3) is **2n³ - 3n² - 7n + 3**.