Problem 104 - Introductory Algebra for College Students

Question

Explain how to simplify \(4 x^{2}+6 x^{2} .\) Why is the sum not equal to \(10 x^{4} ?\)

Step-by-Step Solution

Answer

The simplified form of \(4x^2 + 6x^2\) is \(10x^2\). It's not equal to \(10x^4\) because the exponents don't add up when adding like terms. The exponents stay the same.

Step 1: Identify Like Terms

In algebra, like terms are terms that contains the same variables raised to the same power. So, \(4x^2\) and \(6x^2\) are like terms because they have the same variable \(x\) and the same exponent 2.

Step 2: Add Like Terms

The coefficient of the like terms are added together while the rest of the term (the variable and the exponent) remains the same. So \(4x^2 + 6x^2\) results in \(10x^2\).

Step 3: Explain Difference in Exponents

The sum of \(4x^2 + 6x^2\) can never yield \(10x^4\) because the exponents themselves don't add up. When adding like terms, the variable and the exponent stay the same, we only added the coefficients. The exponent only changes if the terms are being multiplied, not added.