multiply (2√3 − √6)^2
To multiply the expression (2√3 − √6)^2, we can use the distributive property.
(2√3 − √6)^2 = (2√3 − √6)(2√3 − √6)
To simplify this expression, we can use the FOIL method.
(2√3 − √6)(2√3 − √6)
= (2√3)(2√3) + (2√3)(-√6) + (-√6)(2√3) + (-√6)(-√6)
= 4(√3)(√3) - 2(√3)(√6) - 2(√3)(√6) + 6
= 4(√3)^2 - 4(√3)(√6) + 6
= 4(3) - 4(√3√6) + 6
= 12 - 4√18 + 6
= 18 - 4√18
Therefore, (2√3 − √6)^2 simplifies to 18 - 4√18.
To multiply the expression (2√3 − √6)^2, we can use the formula (a - b)^2 = a^2 - 2ab + b^2.
Let's substitute a = 2√3 and b = √6 into the formula.
(a - b)^2 = (2√3 - √6)^2
= (2√3)^2 - 2(2√3)(√6) + (√6)^2
= 4(3) - 2(2√3)(√6) + 6
= 12 - 2(2)(√18) + 6
= 12 - 4√18 + 6
Simplifying further, we have:
= 18 - 4√18
= 18 - 4√(9 * 2)
= 18 - 4(3√2)
= 18 - 12√2
So, (2√3 - √6)^2 = 18 - 12√2.
To multiply (2√3 − √6)^2, we can use the concept of the distributive property.
Step 1: Start by multiplying the two terms inside the bracket together using the distributive property.
(2√3 - √6) * (2√3 - √6)
Step 2: Multiply the first term in the first bracket (2√3) by both terms in the second bracket (2√3 - √6).
2√3 * 2√3 = 4 * 3 = 12
2√3 * -√6 = -2√18 = -2√(3 * 6) = -2√(18) = -2√(9 * 2) = -2 * 3√2 = -6√2
Step 3: Multiply the second term in the first bracket (-√6) by both terms in the second bracket (2√3 - √6).
-√6 * 2√3 = -2√(6 * 3) = -2√(18) = -2√(9 * 2) = -2 * 3√2 = -6√2
-√6 * -√6 = √(6 * 6) = √(36) = √(6 * 6) = √(6^2) = 6
Step 4: Combine these results together.
12 - 6√2 - 6√2 + 6
12 - 12√2 + 6
18 - 12√2
So, (2√3 − √6)^2 equals 18 - 12√2.