Note: When typing your work, use "sqrt" to represent the radical symbol, followed by parentheses to enclose anything under that radical. (6−3–√)(3+3–√)
To simplify the expression (6−3–√)(3+3–√), we can use the distributive property.
First, let's distribute the terms inside the first set of parentheses to the terms inside the second set of parentheses:
(6−3–√)(3+3–√)
= 6(3) + 6(3) - 6√3 - 3(3) - 3(3) + 3√3 – √(3)(3) – √(3)(3)
= 18 + 18 - 6√3 - 9 - 9 + 3√3 – 3√3 – 3√3
= (18 + 18 - 9 - 9) + (-6√3 + 3√3 - 3√3 - 3√3)
= 36 - 18√3 - 12√3
= 36 - 30√3
Therefore, (6−3–√)(3+3–√) simplifies to 36 - 30√3.