can you help with math please?

Question

multiply using teh vertical method.

(m^2-5mn+3n^2 )(m^2+4mn-2n^2)

Answer 1

Write your first expression vertically:
m²
-5mn
3n²

Now multiply the second expression by each of these, one by one:
m² (m² + 4mn - 2n²) --> m^4 + 4m^3n - 2m²n²
-5mn (m² + 4mn - 2n²) --> -5m^3n - 20m²n² + 10mn^3
3n² (m² + 4mn - 2n²) --> 3m²n² + 12mn^3 - 6n^4

It helps if you write the results staggered as shown because then the same terms are lined up vertically.
m^4 + 4m^3n - 2m²n²
........ -5m^3n - 20m²n² + 10mn^3
...................... 3m²n² + 12mn^3 - 6n^4

From here it is easy to add the expressions up, just adding them vertically:

m^4 - m^3n - 19m²n² + 22mn^3 - 6n^4