(2x-1)(4x^2+2x+1)-7(x^3+1)

2 min read Jun 07, 2024

Expansion of a Complex Algebraic Expression

In this article, we will be expanding a complex algebraic expression involving binomials and trinomials. The expression is:

$(2x-1)(4x^2+2x+1)-7(x^3+1)$

Let's break it down step by step.

We will start by expanding the first part of the expression, which is the product of two binomials:

$(2x-1)(4x^2+2x+1)$

Using the distributive property, we get:

$= 2x(4x^2+2x+1) - (4x^2+2x+1)$

$= 8x^3 + 4x^2 + 2x - 4x^2 - 2x - 1$

Now, let's simplify the expression by combining like terms:

$= 8x^3 + (4x^2 - 4x^2) + (2x - 2x) - 1$

$= 8x^3 - 1$

Now, let's move on to the second part of the expression:

$-7(x^3+1)$

Using the distributive property again, we get:

$= -7x^3 - 7$

Now that we have expanded both parts, let's combine them:

$= (8x^3 - 1) - (7x^3 + 7)$

Finally, let's simplify the final expression by combining like terms:

$= x^3 - 8$

And that's our final answer!

$\boxed{(2x-1)(4x^2+2x+1)-7(x^3+1) = x^3 - 8}$