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Chapter 10: Problem 122

Will help you prepare for the material covered in the next section. a. Simplify: \(21 x+10 x\) b. Simplify: \(21 \sqrt{2}+10 \sqrt{2}\)

Short Answer

Expert verified
The simplified form of the expressions given in a and b are \(31x\) and \(31\sqrt{2}\) respectively.

Step by step solution

01

Simplification of Algebraic Expression

For the first expression \(21x + 10x\), both terms are like terms as they have the same variable \(x\). Like terms can be combined by performing the operations of their coefficients (21 and 10, in this case). The operation to perform here is addition. We add 21 and 10 to get 31. Hence, the simplified form of \(21x + 10x\) is \(31x\).
02

Simplification of Square Roots

For the second expression \(21\sqrt{2} + 10\sqrt{2}\), the terms can be combined just like the first expression. Here both terms, \(21\sqrt{2}\) and \(10\sqrt{2}\), are like terms as they have the same square root \(\sqrt{2}\). The like terms can be combined by adding the coefficients 21 and 10 to obtain 31. So, the simplified form of the this expression is \(31\sqrt{2}\).

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