Final answer:
To expand the given expression, apply the distributive property, multiply term by term, and simplify to get 3√2 × x² - 3√6.
Step-by-step explanation:
To expand the expression √3×x + √3)(√6×x - √6), we will apply the distributive property, also known as the FOIL method. This method stands for First, Outer, Inner, Last, which are the terms we will multiply:
- First terms: √3 × x * √6 × x = 3√2 × x²
- Outer terms: √3 × x * -√6 = -3√6 × x
- Inner terms: √3 * √6 × x = 3√6 × x
- Last terms: √3 * -√6 = -3√6
Combining these, we get 3√2 × x² - 3√6 × x + 3√6 × x - 3√6.
Simplifying by combining like terms, we are left with:
3√2 × x² - 3√6