(2n-3)(4n^2-2n+4)

3 min read Jun 16, 2024

Expanding the Expression (2n-3)(4n^2-2n+4)

This article will guide you through expanding the expression (2n-3)(4n^2-2n+4) using the distributive property and FOIL method.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. In other words:

a(b + c) = ab + ac

Expanding using the Distributive Property

We can apply the distributive property twice to expand the given expression:

First Distribution: Treat (4n^2-2n+4) as a single term and multiply it by 2n and -3 separately.
```
(2n-3)(4n^2-2n+4) = 2n(4n^2-2n+4) - 3(4n^2-2n+4) 
```
Second Distribution: Distribute 2n and -3 to each term inside the parentheses.
```
= (8n^3 - 4n^2 + 8n) + (-12n^2 + 6n - 12)
```

Expanding using the FOIL Method

The FOIL method is a shortcut for expanding two binomials. It stands for First, Outer, Inner, Last.

First: Multiply the first terms of each binomial: 2n * 4n^2 = 8n^3
Outer: Multiply the outer terms of each binomial: 2n * 4 = 8n
Inner: Multiply the inner terms of each binomial: -3 * -2n = 6n
Last: Multiply the last terms of each binomial: -3 * 4 = -12

Combining all the terms:

(2n-3)(4n^2-2n+4) = 8n^3 + 8n + 6n - 12 - 4n^2 - 12n^2

Simplifying the Expression

After expanding, we can combine like terms:

= 8n^3 - 16n^2 + 14n - 12

Conclusion

Therefore, the expanded form of (2n-3)(4n^2-2n+4) is 8n^3 - 16n^2 + 14n - 12. We can achieve this by applying the distributive property or the FOIL method.