Ex. Find the value of 84 -7[- 11x-4{- 17x + 3(8-9 -5x)}].
The expression = 84 - 7 [- 11 x - 4{ - 17 x + 3 (8 -9 + 5x)}] = 84 - 7 [ - 11 x - 4 { - 17 X + 3 (5x - 1)}] =84-7[-11x-4{-17x+ 15x-3}] = 84-7[- 11x-4{ -2x-3}] = 84-7[- 11x- 8x+12] = 84-7[-3 + 12] = 84 + 21x-84 = 21x . When the beginner has had a little practice, the number of steps may be considerably diminished.
EXAMPLES VI. b.
Simplify by removing brackets :
1. a - [2b + {3 c - 3 a - (a + b)} + 2 a - ( b+ 3 c)]. 2. a + b- (c + a - [ b+ c - (a +b - {c + a - (b+ c - a)})]). 3. a -(b-c)- [a - b - c - 2 {b+ c - 3 (c - a) - d}]. 4. 2x-(y-4z)-{2x- (3 y + 4z )} - {3 - (4 z+ 2 x)}. 5. b + c - (a + b -[c + a - (b + c - {a + b -(c + a - b)})]). 6. a-(b-c)-[a-b-c~2{b + c}]. 7. 3 a^2 - [6 a^2 - {8 b^2 - (9 c^2 - 2 a^2)}] . 8. b- (c - a) - [ b- a - c - 2{c + a - 3 (a - b) - d}. 9. -20 (a - d) + 3 (b - c) - 2 [ b+ c + d- 3{c + d - 4 (d - a)}]. 10. - 4 (a + d) + 24 (b-c) - c) - 2 [c + d + a - 3 (d + a - 4 ( b+ c)}]. 11. - 10(a + d)-[c+ a + b-3{a + 2b- (c + a- b)}]+ 4c. 12. a - 2 (b - c) -[- {- (4a - b - c - 2{a+ b+ c})}]. 13. 2(3b-5a)-7[a-6{2-5(a-b)}]. 14. 6 {a - 2 [6 - 3 (c + d)]} - 4{a - 3 [- 4 (c - d)]}. 15. 5 {a - 2 [a - 2 (a + x)]} - 4{a - 2 [a - 2 (a + x)]}. 16. - 10 {a - 6 [a - (b- c)]} + 60 {b - (c + a)}. 17. - 3 { - 2 [- 4 (- a)]} 4- 5{ - 2 [- 2 (- a)]}. 18. -2{-[-(x-y)]} + {-2[-(x-y)]}.
