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 - $\frac{1}{x}$

(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.

9th Grade Math

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