¬=Square root
How is [3*(¬2)+2*(¬3)]^2 expanded?
I don't know if this is right or not, but I think its binomial expansion.
you could do the binomial expansion, you also could multiply the factors by FOIL>
(3sqrt2+2sqrt3)(3sqrt2+2sqrt3)
thanks
To expand the expression [3*(√2) + 2*(√3)]^2, we follow the order of operations, which is parentheses, exponents, multiplication/division, and addition/subtraction.
Step 1: Simplify the expression inside the parentheses.
3*(√2) + 2*(√3) can be rewritten as (√2)*(3) + (√3)*(2).
Step 2: Multiply the terms inside the parentheses.
(√2)*(3) + (√3)*(2) equals to 3√2 + 2√3.
Step 3: Square the expression obtained.
(3√2 + 2√3)^2 is equivalent to (3√2 + 2√3) * (3√2 + 2√3).
Step 4: Apply the distributive property.
(3√2 + 2√3) * (3√2 + 2√3) can be expanded as:
(3√2 * 3√2) + (3√2 * 2√3) + (2√3 * 3√2) + (2√3 * 2√3).
Step 5: Simplify each term.
(3√2 * 3√2) = 3^2 * (√2)^2 = 9 * 2 = 18.
(3√2 * 2√3) = 3√2 * 2√3 = 6√6.
(2√3 * 3√2) = 2√3 * 3√2 = 6√6.
(2√3 * 2√3) = 2^2 * (√3)^2 = 4 * 3 = 12.
Step 6: Combine like terms.
18 + 6√6 + 6√6 + 12 equals to 30 + 12√6.
Therefore, the expanded form of [3*(√2) + 2*(√3)]^2 is 30 + 12√6.