Let's simplify the given expression step by step:

Given expression:
$(m - 2n)(m + 1) - 3m(m - 2n)$

1. Expand the first term $(m - 2n)(m + 1)$: $(m - 2n)(m + 1) = m(m + 1) - 2n(m + 1)$ $= m^2 + m - 2nm - 2n$ So, $(m - 2n)(m + 1) = m^2 + m - 2nm - 2n$.

2. Expand the second term $-3m(m - 2n)$: $-3m(m - 2n) = -3m^2 + 6mn$

3. Combine all the terms: $(m^2 + m - 2nm - 2n) - (3m^2 - 6mn)$ Distribute the negative sign: $= m^2 + m - 2nm - 2n - 3m^2 + 6mn$

4. Combine like terms: $= (m^2 - 3m^2) + (m + 6mn - 2nm) - 2n$ $= -2m^2 + (m + 4mn) - 2n$

So, the simplified expression is:
$-2m^2 + m + 4mn - 2n$

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. Simplify $(x - y)(x + y) - 2x(x - y)$.
2. Expand and simplify $(a + 3b)(a - 2) - 4a(a + 3b)$.
3. Factor $-2m^2 + m + 4mn - 2n$.
4. Simplify $(p - q)(p + r) - 5p(p - q)$.
5. Combine like terms in $-4x^2 + 3x + 7xy - 2x^2 - 2x + 5xy$.

Tip: Always expand the expressions fully before combining like terms to ensure the correct simplification.