Question

If `M=5x^{2}+7x-4`and `N=-3x^{2}-4x+5`then what is M+N?

Answer 1

Find the product of 5−3y2y−3. Use Algebra tiles if needed. Write your product in standard form.

Answer 2

To find \( M + N \), we will add the two given polynomials \( M \) and \( N \).

Given:
\[
M = 5x^{2} + 7x - 4
\]
\[
N = -3x^{2} - 4x + 5
\]

Now, we will add \( M \) and \( N \):

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

Combining like terms:

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

2. For \( x \) terms:
\[
7x - 4x = 3x
\]

3. For constant terms:
\[
-4 + 5 = 1
\]

Now, putting it all together:
\[
M + N = 2x^{2} + 3x + 1
\]

Thus, the result is:
\[
\boxed{2x^{2} + 3x + 1}
\]

Answer 3

To find the product of the expressions \(5 - 3y\) and \(2y - 3\), we will use the distributive property (also known as the FOIL method for binomials).

We will multiply each term in the first expression by each term in the second expression:

\[
(5 - 3y)(2y - 3)
\]

1. **First**: Multiply the first terms:
\[
5 \cdot 2y = 10y
\]

2. **Outer**: Multiply the outer terms:
\[
5 \cdot (-3) = -15
\]

3. **Inner**: Multiply the inner terms:
\[
-3y \cdot 2y = -6y^2
\]

4. **Last**: Multiply the last terms:
\[
-3y \cdot (-3) = 9y
\]

Now, we combine all these results:

\[
10y + (-15) + (-6y^2) + 9y
\]

Combining like terms:

- For \(y^2\) terms, we only have \(-6y^2\).
- For \(y\) terms:
\[
10y + 9y = 19y
\]
- The constant term is \(-15\).

Putting it all together, we have:

\[
-6y^2 + 19y - 15
\]

Thus, the product in standard form is:

\[
\boxed{-6y^2 + 19y - 15}
\]