estion 3
of 8 Step 1 of 1

Iltiply and simplify the following radical expressions. Assume all variables are positive.

Keyboard

Ask by Thornton Cole. in the United States

Mar 21,2025

Question

estion 3
of 8 Step 1 of 1

Iltiply and simplify the following radical expressions. Assume all variables are positive.

Keyboard

Ask by Thornton Cole. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

1. Recognize that the given expression is a product of two identical binomials:
   $$
   (\sqrt{w} - \sqrt{x})^2
   $$

2. Use the formula for squaring a binomial:
   $$
   (a - b)^2 = a^2 - 2ab + b^2
   $$
   Here, $$a = \sqrt{w}$$ and $$b = \sqrt{x}$$.

3. Compute each term:
   - $$a^2 = (\sqrt{w})^2 = w$$
   - $$2ab = 2(\sqrt{w})(\sqrt{x}) = 2\sqrt{wx}$$
   - $$b^2 = (\sqrt{x})^2 = x$$

4. Substitute the computed terms back into the formula:
   $$
   (\sqrt{w} - \sqrt{x})^2 = w - 2\sqrt{wx} + x
   $$
$$ w - 2\sqrt{wx} + x $$