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convolution of the following functions?

(u[n] - u[n-5]) * (u[n] - u[n-5])

In order to solve it I said:

u[n] - u[n-5] = δ[n] + δ[n-1] + δ[n-2] + δ[n-3] + δ[n-4]

and the answer is

δ[n] + 2δ[n-1]+ 3 δ[n-2] + 4δ[n-3] + 5δ[n-4] + 4δ[n-5] + 3δ[n-6] + 2δ[n-7] + δ[n-8]

but I was wondering is there a way to use the convolutional sum with the unit step functions instead of impulses?

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