¡Ì means sqrt.

Simplify (2¡Ì6+3¡Ì3)(¡Ì6-5¡Ì3)
I got 15¡Ì2 -45.

(2sqrt6 + 3sqrt3)(sqrt6-5sqrt3)

FOIL...
2*6-10sqrt18+3sqrt18-15*3
12-7sqrt18-45
but sqrt 18=3sqrt2
-33+21sqrt2
check my work

how does sqrt 18=3sqrt2?

To simplify the expression (2√6+3√3)(√6-5√3), you can use the distributive property of multiplication.

Step 1: Distribute the first term (2√6) to both terms in the second parentheses (√6 and -5√3):
(2√6)(√6) + (2√6)(-5√3)

Step 2: Distribute the second term (3√3) to both terms in the second parentheses (√6 and -5√3):
(3√3)(√6) + (3√3)(-5√3)

Step 3: Simplify each term:
2√6 * √6 = 2√(6 * 6) = 2√36 = 2 * 6 = 12
2√6 * -5√3 = -10√(6 * 3) = -10√18 = -10√(9 * 2) = -10 * 3√2 = -30√2

3√3 * √6 = 3√(3 * 6) = 3√18 = 3√(9 * 2) = 3 * 3√2 = 9√2
3√3 * -5√3 = -15√(3 * 3) = -15√9 = -15 * 3 = -45

Step 4: Combine like terms:
12 - 30√2 + 9√2 - 45 = -33√2 - 33

So, the simplified expression is -33√2 - 33. It seems that you made an error in your calculation.