Multiply and simplify

(9square root 6 - 4 square root 10)
(square root 6 - 7 square root 10)
I have been stumped and working on all day. Any suggestions?

(9√6 - 4√10)(√6 - 7√10)

= 9√36 - 63√60 - 4√60 + 28√100
= 54 - 67√60 + 280
= 334 - 67√4√15
= 334 - 134√15

To multiply and simplify the given expression, we can use the distributive property. Let's break it down step by step:

Given expression: (9√6 - 4√10)(√6 - 7√10)

Step 1: Distribute the first term (9√6) to both terms in the second parentheses:
9√6 * √6 - 9√6 * 7√10

Step 2: Distribute the second term (-4√10) to both terms in the second parentheses:
-4√10 * √6 - 4√10 * 7√10

Step 3: Simplify each term separately by multiplying together the numbers outside the square roots and combining the square roots:
(9 * 6 * √6 * √6) - (9 * 7√10 * √6) - (4 * 10 * √10 * √6) - (4 * 7√10 * 7√10)

Step 4: Simplify the square roots:
54 - 63√60 - 40√60 - 196

Step 5: Combine like terms:
54 - 196 - (63 + 40)√60

Step 6: Simplify the constants:
-142 - 103√60

Your final simplified expression is -142 - 103√60.