Question

subtract and simplify.
$(y^2 - 3y - 5) - (-y^2 - 7y + 4)$
$\circ \\ -2y^2 - 7y + 1$
$\circ \\ 2y^2 - 10y + 4$
$\circ \\ 2y^2 + 4y - 9$
$\circ \\ -2y^2 - 10y - 1$

Explanation:

Step1: Distribute the negative sign

To subtract the second polynomial from the first, we distribute the negative sign to each term in the second polynomial:
$$(y^2 - 3y - 5) - (-y^2 - 7y + 4) = y^2 - 3y - 5 + y^2 + 7y - 4$$

Step2: Combine like terms

• For the \(y^2\) terms: \(y^2 + y^2 = 2y^2\)
• For the \(y\) terms: \(-3y + 7y = 4y\)
• For the constant terms: \(-5 - 4 = -9\)

Putting it all together, we get:
$$2y^2 + 4y - 9$$

Answer:

\(2y^2 + 4y - 9\) (corresponding to the option "2\(y^2\) + 4\(y\) − 9")