GB-39-03-001 · Expanding surd brackets

Expand and simplify $(3+\sqrt{2})(12-\sqrt{2})$ .

Surds: Expanding Double Brackets (Grid Method) Booklet p. 46 & p. 48

Method

1) Use a 2×2 multiplication grid (remember √a × √a = a)

2) Collect rational numbers and surd terms

Worked Example (GB-39-03-001)

Surds 2×2 Grid (Booklet p. 46 — remember

\sqrt{2} \times \sqrt{2} = 2

×	$3$	$+\sqrt{2}$
$12$	$36$	$+12\sqrt{2}$
$-\sqrt{2}$	$-3\sqrt{2}$	$-2$

Collect numbers and surds:

(36 - 2) + (12 - 3)\sqrt{2}

34 + 9\sqrt{2}