Question

topic 2: simplifying polynomials

1. $(y^2 + 4y - 1) + (5y^2 + 2)$

Explanation:

Step1: Remove parentheses

To simplify the polynomial, we first remove the parentheses. Since there is a plus sign in front of both parentheses, the signs of the terms inside remain the same. So we have:
\(y^{2}+4y - 1+5y^{2}+2\)

Step2: Combine like terms

Next, we combine the like terms. The like terms for \(y^{2}\) are \(y^{2}\) and \(5y^{2}\), and the constant terms are \(- 1\) and \(2\).
For the \(y^{2}\) terms: \(y^{2}+5y^{2}=(1 + 5)y^{2}=6y^{2}\)
For the constant terms: \(-1 + 2=1\)
The term \(4y\) does not have any like terms to combine with, so it remains as is.
Putting it all together, we get: \(6y^{2}+4y + 1\)

Answer:

\(6y^{2}+4y + 1\)