Problem 143 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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 \(16x^{8} + 6x^{5}\).