Question

simplify each expression by determining the sum or difference.\\((5x^2 + 2x - 3) + (2x^2 - 3x)\\)\\(\text{must show all work for credit}\\)\\(\text{type a response}\\)

Explanation:

Step1: Remove parentheses

We remove the parentheses from the expression \((5x^{2}+2x - 3)+(2x^{2}-3x)\). Since there is a plus sign in front of both parentheses, the terms inside remain as they are. So we get \(5x^{2}+2x - 3+2x^{2}-3x\).

Step2: Combine like terms

• For the \(x^{2}\) terms: We have \(5x^{2}\) and \(2x^{2}\). Combining them, we use the rule of adding coefficients of like terms. So \(5x^{2}+2x^{2}=(5 + 2)x^{2}=7x^{2}\).
• For the \(x\) terms: We have \(2x\) and \(-3x\). Combining them, \(2x-3x=(2 - 3)x=-x\).
• The constant term is \(-3\) (since there are no other constant terms to combine with it).

Putting it all together, we have \(7x^{2}-x - 3\).

Answer:

\(7x^{2}-x - 3\)