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Chapter 0: Problem 150

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

Short Answer

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

Step by step solution

01

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 \(31x\).
02

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 \(31\sqrt{2}\).

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