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Chapter 5: Problem 28

Multiply the monomials. $$(10 x)\left(3 x^{2}\right)$$

Short Answer

Expert verified
The result of the multiplication of the monomials \(10 x\) and \(3 x^{2}\) is \(30 x^{3}\).

Step by step solution

01

Multiply Constants

We first multiply the constants 10 and 3 together. This gives us \(10 * 3 = 30\). The product of 10 and 3 is 30.
02

Multiply Variables

Next, we multiply variable \(x\) from the first monomial with \(x^{2}\) from the second monomial. Applying the rule of exponents, \(x^{m} * x^{n} = x^{m + n}\), we get \(x * x^{2} = x^{1+2} = x^{3}\).
03

Combine Coefficients and Variables

Finally, we combine the results obtained from step 1 and step 2. This consists of the multiplied coefficient, 30, and the variable portion, \(x^{3}\). So, the result is \(30 x^{3}\).

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