Chapter 8.2, Problem 45HP

To determine

To state: If Pearl and Ted either of them correct? Explain the reasoning.

Answer to Problem 45HP

Ted’s work is correct.

Explanation of Solution

Given:

  

Calculation:

The given expression is $2x^2\left(3x^2+4x+2\right)$

Distributing $2x^2$ over the parenthesis

  $\begin{array}{l}2x^2\cdot 3x^2+2x^2\cdot 4x+2x^2\cdot 2\\ =6x^4+8x^3+4x^2\end{array}$

Pearl did a mistake while multiplying $2x^2$ with $4x$ . It should be $8x^3$ instead of $8x^2$ .

When the same base is multiplying then the exponents gets added. This is the product rule of exponent.

Ted work is absolutely correct.

So, only Ted’s work is correct.