First, let's simplify the left side of the equation:

(1-m)(1-m²) + m(m+1)
= (1-m)(1-m)(1+m) + m(m+1)
= (1-m)²(1+m) + m(m+1)
= (1 - 2m + m²)(1+m) + m(m+1)
= (1 + m² - 2m - 2m² + 4m - 2m²) + m(m+1)
= (1 - 4m - 3m²) + (m² + m)
= 1 - 4m - 3m² + m² + m
= 1 - 3m - 2m² + m
= 1 - 2m - 2m²

Now, let's simplify the right side of the equation:

m² + 1

Since the simplified left side is equal to the simplified right side, the equation is true:

1 - 2m - 2m² = m² + 1