Question

Expand:

`(4sqrt(5) + 3sqrt(7))^2`

Answer 1

Let’s expand:

`(4sqrt(5) + 3sqrt(7))^2`

Use the identity:

(a + b)² = a² + 2ab + b²

Let:

• `a = 4sqrt(5)`
• `b = 3sqrt(7)`

Now compute each term:

• `a^2 = (4sqrt(5))^2 = 16 xx 5 = 80`
• `2ab = 2 xx 4sqrt(5) xx 3sqrt(7) = 24sqrt(35)`
• `b^2 = (3sqrt(7))^2 = 9 xx 7 = 63`

Now add them:

`(4sqrt(5) + 3sqrt(7))^2`

= `80 + 24sqrt(35) + 63`

= `143 + 24sqrt(35)`