Multiply and simplify. $$ \begin{array}{l}(\sqrt{x}-\sqrt{2})(\sqrt{x}+\sqrt{2})=x-2 \ (5 \sqrt{x}-\sqrt{2})^{2}= ext { II }\end{array} $$

Question

Multiply and simplify. $$ \begin{array}{l}(\sqrt{x}-\sqrt{2})(\sqrt{x}+\sqrt{2})=x-2 \ (5 \sqrt{x}-\sqrt{2})^{2}=	ext { II }\end{array} $$

UpStudy AI · Accepted Answer

Let's simplify the expression $$ (5\sqrt{x} - \sqrt{2})^{2} $$.

### Step 1: Apply the Square of a Binomial Formula
The formula for squaring a binomial is:
$$
(a - b)^2 = a^2 - 2ab + b^2
$$
Here, $$ a = 5\sqrt{x} $$ and $$ b = \sqrt{2} $$.

### Step 2: Calculate Each Term
1. **First Term ($$ a^2 $$):**
$$
(5\sqrt{x})^2 = 25x
$$

2. **Middle Term ($$ -2ab $$):**
$$
-2 \times 5\sqrt{x} \times \sqrt{2} = -10\sqrt{2x}
$$

3. **Last Term ($$ b^2 $$):**
$$
(\sqrt{2})^2 = 2
$$

### Step 3: Combine the Terms
Putting it all together:
$$
(5\sqrt{x} - \sqrt{2})^2 = 25x - 10\sqrt{2x} + 2
$$

### Final Simplified Form
$$
25x - 10\sqrt{2x} + 2
$$
$$ 25x - 10\sqrt{2x} + 2 $$

Multiply and simplify.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Step 1: Apply the Square of a Binomial Formula

Step 2: Calculate Each Term

Step 3: Combine the Terms

Final Simplified Form

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions