Problem 44 - Elementary Algebra

Question

\(\left(7 x^{2}-15\right)+(2 x-3)\)

Step-by-Step Solution

Answer

The simplified expression is \(7x^{2} + 2x - 18\).

Step 1: Arrange the terms

First, identify and arrange the terms in the expression \(7x^{2} - 15 + 2x - 3\). Separate into like terms.

Step 2: Combine the constant terms

Combine the constant terms \(-15\) and \(-3\) to get \(-18\).

Step 3: Write the final simplified expression

After combining the like terms, the simplified expression is \(7x^{2} + 2x - 18\).

Key Concepts

like terms

Understanding the concept of 'like terms' is essential in algebra. Like terms are terms that have the same variable raised to the same power. For instance, in the expression \(7x^{2} - 15 + 2x - 3\), the terms \(7x^{2}\) and \(2x\) are not like terms because \(7x^{2}\) has the variable \(x\) raised to the power of 2, whereas \(2x\) has the variable \(x\) raised to the power of 1. On the other hand, constants like \(-15\) and \(-3\) are like terms because they are both constant terms without any variables attached.

constant terms

Constant terms are numbers without variables. In the equation \(7x^{2} - 15 + 2x - 3\), the constants are \(-15\) and \(-3\). They provide a fixed value in the expression. Combining constant terms is straightforward since they are like terms by nature. This means you can simply add or subtract them.

combining terms

Combining terms is the process of simplifying an algebraic expression by adding or subtracting like terms. Here’s what you do:

• Identify terms that have the same variables raised to the same power.
• Combine these like terms by adding or subtracting their coefficients (numerical values in front of the variables).
• Don’t forget to also combine constant terms, which are numbers on their own.

For instance, from \(7x^{2} - 15 + 2x - 3\), combining the constant terms gives us \(-18\). Simplifying the entire expression results in \(7x^{2} + 2x - 18\). This process helps in making the expression easier to work with in further calculations or whenever you need the most simplified form.