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

Answer 1

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 2

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

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:

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