The problem requires us to subtract the polynomial $(5.6x^3 - 7.2x^2 + 2)$ from the polynomial $(2.2x^3 - 5.4x^2 - 2)$. We need to simplify the resulting expression.

1. Problem Description

The problem requires us to subtract the polynomial $(5.6x^3 - 7.2x^2 + 2)$ from the polynomial $(2.2x^3 - 5.4x^2 - 2)$. We need to simplify the resulting expression.

2. Solution Steps

First, we distribute the negative sign to each term within the second polynomial:

$(2.2x^3 - 5.4x^2 - 2) - (5.6x^3 - 7.2x^2 + 2) = 2.2x^3 - 5.4x^2 - 2 - 5.6x^3 + 7.2x^2 - 2$

Next, we group like terms:

$(2.2x^3 - 5.6x^3) + (-5.4x^2 + 7.2x^2) + (-2 - 2)$

Then, we combine like terms:

$(2.2 - 5.6)x^3 + (-5.4 + 7.2)x^2 + (-2 - 2)$

$-3.4x^3 + 1.8x^2 - 4$

3. Final Answer

The simplified expression is $-3.4x^3 + 1.8x^2 - 4$.