Expand and simplify (√20 + 2√10)(3√6 − √3)

Sure, let's expand and simplify the expression step by step.

Step 1: Expand the expression

(√20 + 2√10)(3√6 − √3) = √203√6 - √20√3 + 2√103√6 - 2√10√3

Step 2: Simplify each term

= 3√120 - √60 + 6√60 - 2√30

Step 3: Simplify the square roots

= 32√30 - 2√30 + 62√15 - 2√30

Step 4: Simplify the expression

= 6√30 - 2√30 + 12√15 - 2√30

Step 5: Combine like terms

= 2√30 + 12√15

So, (√20 + 2√10)(3√6 − √3) simplifies to 2√30 + 12√15.