Problem 150 - College Algebra

Question

a. Simplify: \(21 x+10 x\) b. Simplify: \(21 \sqrt{2}+10 \sqrt{2}\)

Step-by-Step Solution

Answer

The simplified form of \(21x + 10x\) is \(31x\) and \(21\sqrt{2} + 10\sqrt{2}\) is \(31\sqrt{2}\).

Step 1: Simplify Algebraic Expression 1

First exercise involves combining the terms that are similar, that is \(21x\) and \(10x\). This can be done easily by adding their coefficients, which are 21 and 10. So, \(21x + 10x = (21 + 10)x = 31x\). So, \(21x + 10x\) simplifies to \(31x\).

Step 2: Simplify Algebraic Expression 2

The second part is similar to the first one. However, instead of x, we have \(\sqrt{2}\). To simplify \(21\sqrt{2} + 10\sqrt{2}\), add the coefficients which are 21 and 10. So, \(21\sqrt{2} + 10\sqrt{2} = (21 + 10)\sqrt{2} = 31\sqrt{2}\). Therefore, \(21\sqrt{2} + 10\sqrt{2}\) simplifies to \(31\sqrt{2}\).