Multiply and simplify if possible. Show ALL work to receive credit.%0D%0A%0D%0ANote: When typing your work, use "sqrt" to represent the radical symbol, followed by parentheses to enclose anything under that radical.%0D%0A%0D%0A(6−3–√)(3+3–√)

Question

Multiply and simplify if possible. Show ALL work to receive credit.%0D%0A%0D%0ANote: When typing your work, use "sqrt" to represent the radical symbol, followed by parentheses to enclose anything under that radical.%0D%0A%0D%0A(6−3–√)(3+3–√)

Answer 1

To multiply and simplify (6−3–√)(3+3–√), we can use the distributive property.

First, let's simplify the expressions within the parentheses separately:

6−3–√ = 6−(3–√) = 6−3+√ = 3+√

3+3–√ = 6−√

Now, we can multiply these simplified expressions:

(3+√)(6−√)

Using the FOIL method (first, outer, inner, last), we can multiply these binomials:

First: 3 × 6 = 18
Outer: 3 × -√ = -3√
Inner: √ × 6 = 6√
Last: √ × -√ = -√² = -√

Combining these terms, we have:

18 - 3√ + 6√ - √

Simplifying further:

18 + (6√ - 3√ - √)

Combining like terms:

18 + 3√ - √

= 18 + 2√

So, (6−3–√)(3+3–√) simplifies to 18 + 2√.