Question

and subtracting algebraic radical expressions
ind the difference: $8ab\sqrt3{ac^2} - 14ab\sqrt3{ac^2}$
$22\sqrt3{ac^2}$ $-6ab\sqrt3{ac^2}$ $-22\sqrt3{ac^2}$
$6ab\sqrt{ac^2}$

Explanation:

Step1: Identify like terms

The terms \(8ab\sqrt[3]{ac^2}\) and \(14ab\sqrt[3]{ac^2}\) are like terms (same radical part \(\sqrt[3]{ac^2}\) and same coefficient part \(ab\)).

Step2: Combine like terms

Use the distributive property \(ax - bx=(a - b)x\), where \(a = 8\), \(b = 14\), and \(x = ab\sqrt[3]{ac^2}\).
So, \(8ab\sqrt[3]{ac^2}-14ab\sqrt[3]{ac^2}=(8 - 14)ab\sqrt[3]{ac^2}\).
Calculate \(8-14=-6\), so the result is \(-6ab\sqrt[3]{ac^2}\).

Answer:

\(-6ab\sqrt[3]{ac^2}\) (corresponding to the option with this expression, e.g., if the middle top option is \(-6ab\sqrt[3]{ac^2}\), then the answer is that option: B. \(-6ab\sqrt[3]{ac^2}\) assuming the options are labeled A, B, C, D with A as \(22\sqrt[3]{ac^2}\), B as \(-6ab\sqrt[3]{ac^2}\), C as \(-22\sqrt[3]{ac^2}\), D as \(6ab\sqrt{ac^2}\))