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Worksheet on Expanding of
(a ± b ± c)2 and its Corollaries
Practice the questions given in the worksheet on expanding of (a ± b ± c)2 and its corollaries.
1. Expand the squares of the following trinomials.
(i) a + 2b + 3c
(ii) 2x + 3y + 4z
(iii) x + 2y – 3z
(iv) 3a – 4b – c
(v) 1 – x - 1x
(vi) 1 – a – a2
2. Simplify:
(i) (x + y + z)2 + (x – y + z)2
(ii) (a – 2b – 3c)2 + (2a + 3b – c)2 + (3a – b +2c)2
3. (i) If a + b + c = 6 and ab + bc + ca = 11, find a2 + b2 + c2.
(ii) a + b – c = 7 and ab – bc – ca = 14, find a2 + b2 + c2.
[Hint: a2 + b2 + c2 = a2 + b2 + (-c)2
= (a + b – c)2 – 2{ab + b(-c) + (-c)a}
= (a + b –c)2 – 2(ab – bc – ca)
= 72 – 2 × 14]
(iii) If a2 + b2 + c2 = 50 and ab + bc + ca = 47, find a + b + c.
4. If x + y + z = 12 and x2 + y2 + z2 = 44, find xy + yz + zx.
Answers for the worksheet on on expanding of (a ± b ± c)2 and its corollaries are given below.
Answers
1. (i) a2 + 4b2 + 9c2 + 4ab + 12bc + 6ca
(ii) 4x2 + 9y2 + 16z2 + 12xy + 24yz + 16zx
(iii) x2 + 4y2 + 9z2 + 4xy – 12yz – 6zx
(iv) 9a2 + 16b2 + c2 – 24ab + 8bc – 6ca
(v) x2 + 1x2 – 2x + 2x - 1
(vi) 1 – 2a – a2+ 2a3 + a4
2. (i) 2x2 + 2y2 + 2z2 – 4yz
(ii) 14a2 + 14b2+ 14c2 +2ab + 2bc + 2ca
3. (i) 14
(ii) 21
(iii) ±12
4. 50.
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