M= 5x^2+7x-4 and N = 3x^2 -4x+5. What is the value of M-N

Answer 1

To find the value of \( M - N \), we start with the expressions for \( M \) and \( N \):

\[ M = 5x^2 + 7x - 4 \] \[ N = 3x^2 - 4x + 5 \]

Now, we subtract \( N \) from \( M \):

\[ M - N = (5x^2 + 7x - 4) - (3x^2 - 4x + 5) \]

We distribute the negative sign across the terms in \( N \):

\[ M - N = 5x^2 + 7x - 4 - 3x^2 + 4x - 5 \]

Next, we combine like terms:

1. For \( x^2 \) terms: \[ 5x^2 - 3x^2 = 2x^2 \]

2. For \( x \) terms: \[ 7x + 4x = 11x \]

3. For constant terms: \[ -4 - 5 = -9 \]

Combining all these results, we obtain:

\[ M - N = 2x^2 + 11x - 9 \]

Thus, the final value of \( M - N \) is:

\[ \boxed{2x^2 + 11x - 9} \]