How to derive the answer to this convolution problem?

1. How do you solve convolution sum?
2. Why do we calculate convolution?

How do you solve convolution sum?

Convolution sum and product of polynomials— The convolution sum is a fast way to find the coefficients of the polynomial resulting from the multiplication of two polynomials. Suppose x [ n ] = u [ n ] − u [ n − 3 ] find its Z-transform , a second-order polynomial in .

Why do we calculate convolution?

Convolution is important because it relates the three signals of interest: the input signal, the output signal, and the impulse response.