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Chapter 0: Problem 143

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$2 x^{4}\left(8 x^{4}+3 x\right)$$

Short Answer

Expert verified
The solution to the exercise is \(16x^{8} + 6x^{5}\).

Step by step solution

01

Identification of the Terms.

First, identify the monomial and the polynomial in the expression. Here the monomial is \(2x^4\) and the polynomial is \((8x^4 + 3x)\). This means we have to distribute \(2x^4\) across the terms inside the parentheses.
02

Application of the Distributive Property.

Apply the distributive property to the expression. Multiply the monomial with each term in the polynomial. This gives \(2x^4 \cdot 8x^4 + 2x^4 \cdot 3x\). Simplify this to obtain \(16x^{8} + 6x^{5}\).

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Most popular questions from this chapter

If n is a natural number, what does \(b^{n}\) mean? Give an example with your explanation.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Some rational numbers are not positive.

Factor and simplify each algebraic expression. $$4 x^{-\frac{1}{3}}+8 x^{\frac{1}{3}}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I use the definition for \(a^{\frac{m}{n}},\) I usually prefer to first raise \(a\) to the \(m\) power because smaller numbers are involved.

Factor Completely. $$6 x^{4}+35 x^{2}-6$$
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