Question

Expand and simplify

(4 + root2) (6 - root2)

Give your answer in the form
b + c root2

Answer 1

22 + 2√2

Explanation:

(4 + √2)(6 - √2)

⇒ 4(6 - √2) + √2(6 - √2)

⇒ 24 - 4√2 + 6√2 + (√2× - √2) (√2 × -√2 = -2)

⇒ 24 - 4√2 + 6√2 - 2

⇒ 24 - 2 - 4√2 + 6√2 (collecting like terms together)

⇒ 22 + 2√2 (can't simplify further)

⇒ 11 + √2 (If you divide it by 2) ⇒ Optional