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JAMB Mathematics 2012 Paper

Question : 7

Total: 48

Simplify

(\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2

Solution:

Concept:

Use the difference of two squares identity to simplify the expression without fully expanding each squared bracket.

Explanation:

Let

a = \sqrt{6}

and

b = 2

. The expression becomes

(a + b)^2 - (a - b)^2

Recall the identity

X^2 - Y^2 = (X - Y)(X + Y)

Apply it to

(a + b)^2 - (a - b)^2

: write it as

[(a + b) - (a - b)] \times [(a + b) + (a - b)]

Simplify the first bracket:

(a + b) - (a - b) = a + b - a + b = 2b

Simplify the second bracket:

(a + b) + (a - b) = a + b + a - b = 2a

Multiply the two results:

2b \times 2a = 4ab

Substitute back

a = \sqrt{6}

and

b = 2

4 \times \sqrt{6} \times 2 = 8\sqrt{6}

Answer:

8\sqrt{6}

, which is option C.

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