# 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.

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.

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