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 - \(\frac{1}{x}\)
(vi) 1 – a – a\(^{2}\)
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 a\(^{2}\) + b\(^{2}\) + c\(^{2}\).
(ii) a + b – c = 7 and ab – bc – ca = 14, find a\(^{2}\) + b\(^{2}\) + c\(^{2}\).
[Hint: a\(^{2}\) + b\(^{2}\) + c\(^{2}\) = a\(^{2}\) + b\(^{2}\) + (-c)\(^{2}\)
= (a + b – c)\(^{2}\) – 2{ab + b(-c) + (-c)a}
= (a + b –c)\(^{2}\) – 2(ab – bc – ca)
= 7\(^{2}\) – 2 × 14]
(iii) If a\(^{2}\) + b\(^{2}\) + c\(^{2}\) = 50 and ab + bc + ca = 47, find a + b + c.
4. If x + y + z = 12 and x\(^{2}\) + y\(^{2}\) + z\(^{2}\) = 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) a\(^{2}\) + 4b\(^{2}\) + 9c\(^{2}\) + 4ab + 12bc + 6ca
(ii) 4x\(^{2}\) + 9y\(^{2}\) + 16z\(^{2}\) + 12xy + 24yz + 16zx
(iii) x\(^{2}\) + 4y\(^{2}\) + 9z\(^{2}\) + 4xy – 12yz – 6zx
(iv) 9a\(^{2}\) + 16b\(^{2}\) + c\(^{2}\) – 24ab + 8bc – 6ca
(v) x\(^{2}\) + \(\frac{1}{x^{2}}\) – 2x + \(\frac{2}{x}\) - 1
(vi) 1 – 2a – a\(^{2}\)+ 2a\(^{3}\) + a\(^{4}\)
2. (i) 2x\(^{2}\) + 2y\(^{2}\) + 2z\(^{2}\) – 4yz
(ii) 14a\(^{2}\) + 14b\(^{2}\)+ 14c\(^{2}\) +2ab + 2bc + 2ca
3. (i) 14
(ii) 21
(iii) ±12
4. 50.
From Worksheet on Expanding of (a ± b ± c)^2 and its Corollaries to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Jul 12, 24 03:08 PM
Jul 12, 24 02:11 PM
Jul 12, 24 03:21 AM
Jul 12, 24 12:59 AM
Jul 12, 24 12:30 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.