Question

If M = 10xy +3y−4
and N = 9y+5xy+14
, then what is M−N
?(1 point)
Responses

5xy−6y−18
5 x y minus 6 y minus 18

−5xy−6y−18
negative 5 x y minus 6 y minus 18

5xy+8y+18
5 x y plus 8 y plus 18

5xy+6y−14
5 x y plus 6 y minus 14

15xy+6y+14

Answer 1

To find \( M - N \), we first need to substitute the expressions for \( M \) and \( N \):

\[
M = 10xy + 3y - 4
\]
\[
N = 9y + 5xy + 14
\]

Now we can compute \( M - N \):

\[
M - N = (10xy + 3y - 4) - (9y + 5xy + 14)
\]

Distributing the negative sign into \( N \):

\[
M - N = 10xy + 3y - 4 - 9y - 5xy - 14
\]

Now, combine like terms:

1. For \( xy \) terms:
\[
10xy - 5xy = 5xy
\]

2. For \( y \) terms:
\[
3y - 9y = -6y
\]

3. For the constant terms:
\[
-4 - 14 = -18
\]

Putting it all together, we have:

\[
M - N = 5xy - 6y - 18
\]

Thus, the answer is:

\[
\boxed{5xy - 6y - 18}
\]