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 will substitute the given expressions for \( M \) and \( N \) and simplify.

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

Now, we calculate \( M - N \):

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

Distribute the negative sign in the second term:

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

Now, combine like terms:

1. For the \( xy \) terms: \( 10xy - 5xy = 5xy \)
2. For the \( y \) terms: \( 3y - 9y = -6y \)
3. For the constant terms: \( -4 - 14 = -18 \)

Putting it all together:

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

Thus, the final answer is:

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