Question

Expand:

`(2sqrt(3) - 5sqrt(2))^2`

Answer 1

Let’s expand:

`(2sqrt(3) - 5sqrt(2))^2`

Use the identity:

(a – b)² = a² – 2ab + b²

Let:

• `a = 2sqrt(3)`
• `b = 5sqrt(2)`

Now compute each term:

• `a^2 = (2sqrt(3))^2 = 4 xx 3 = 12`
• `2ab = 2 xx 2sqrt(3) xx 5sqrt(2) = 20sqrt(6)`
• `b^2 = (5sqrt(2))^2 = 25 xx 2 = 50`

Now substitute:

`(2sqrt(3) - 5sqrt(2))^2`

= `12 - 20sqrt(6) + 50`

= `62 - 20sqrt(6)`