Exploring Algebraic Identities — sample questions with answers.

3078 verified exploring algebraic identities questions sit in the bank for this chapter alone. Here are 4 of them, worked; a free account gets a full, board-pattern paper across whichever chapters you pick.

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1 mark Multiple choice

For a = 6 and b = 5 (both positive), which is larger, (a + b)² or a² + b²?

(A) (a + b)²	(B) It depends on which is bigger, a or b.
(C) a² + b²	(D) They are equal.

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(a) (a + b)²

2 marks Short answer

Using (a + b)(a − b), find (i) 34 × 22 and (ii) 208 × 192.

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(i) 748 (ii) 39936

3 marks Short answer

Take three consecutive whole numbers around 16. Add the squares of the smallest and largest, then subtract twice the square of the middle one. Show, using algebra, that the answer is always 2.

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With the numbers n − 1, n, n + 1: (n − 1)² + (n + 1)² − 2n² = (n² − 2n + 1) + (n² + 2n + 1) − 2n² = 2. (Check at n = 16: 225 + 289 − 512 = 2.)

5 marks Long answer

A cuboid has volume (2s² + 8s + 6) cubic units. (i) Take out the common numerical factor. (ii) Factor the quadratic that remains. (iii) Give one possible set of length, breadth and height. (iv) If s = 5, find the numerical volume. (v) Are the three dimensions unique? Explain.

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(i) 2(s² + 4s + 3). (ii) 2(s + 3)(s + 1). (iii) 2, (s + 3), (s + 1). (iv) 96. (v) No — the factor 2 can be attached to any dimension.

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