Simplify each of the following algebraic expression:
i)
ii)
iii)
iv)
v)
vi)
vii)
viii)
ix)
x)
![\hspace{5pt} 5a-[2b-\{2a-4\left(a-2b\right)-3\left(b-\overline{2a-b})\right\}]](https://s0.wp.com/latex.php?latex=%5Chspace%7B5pt%7D+%C2%A0+%C2%A0+5a-%5B2b-%5C%7B2a-4%5Cleft%28a-2b%5Cright%29-3%5Cleft%28b-%5Coverline%7B2a-b%7D%29%5Cright%5C%7D%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "\hspace{5pt} 5a-[2b-\{2a-4\left(a-2b\right)-3\left(b-\overline{2a-b})\right\}]")
![=5a-\left[2b-\left\{2a-4\left(a-2b\right)-3\left(b-2a+b\right)\right\}\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D5a-%5Cleft%5B2b-%5Cleft%5C%7B2a-4%5Cleft%28a-2b%5Cright%29-3%5Cleft%28b-2a%2Bb%5Cright%29%5Cright%5C%7D%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=5a-\left[2b-\left\{2a-4\left(a-2b\right)-3\left(b-2a+b\right)\right\}\right]")
![=5a-[2b-\left\{2a-4a+8b-6b+6a\right\}]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D5a-%5B2b-%5Cleft%5C%7B2a-4a%2B8b-6b%2B6a%5Cright%5C%7D%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=5a-[2b-\left\{2a-4a+8b-6b+6a\right\}]")
![=5a-\left[2b-\left\{4a+2b\right\}\right]=\ 9a](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D5a-%5Cleft%5B2b-%5Cleft%5C%7B4a%2B2b%5Cright%5C%7D%5Cright%5D%3D%5C+9a+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=5a-\left[2b-\left\{4a+2b\right\}\right]=\ 9a")
xi)
xii)
xiii)
xiv)
![\hspace{5pt} 11a-\left[-7m-\left\{6x-\left(4m-\overline{2a-6x}\right)\right\}\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%5Chspace%7B5pt%7D+%C2%A0+11a-%5Cleft%5B-7m-%5Cleft%5C%7B6x-%5Cleft%284m-%5Coverline%7B2a-6x%7D%5Cright%29%5Cright%5C%7D%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "\hspace{5pt} 11a-\left[-7m-\left\{6x-\left(4m-\overline{2a-6x}\right)\right\}\right]")
![=11a-\left[-7m-\left\{6x-\left(4m-2a+6x\right)\right\}\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D11a-%5Cleft%5B-7m-%5Cleft%5C%7B6x-%5Cleft%284m-2a%2B6x%5Cright%29%5Cright%5C%7D%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=11a-\left[-7m-\left\{6x-\left(4m-2a+6x\right)\right\}\right]")
![=11a-\left[-7m-\left\{6x-4m+2a-6x\right\}\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D11a-%5Cleft%5B-7m-%5Cleft%5C%7B6x-4m%2B2a-6x%5Cright%5C%7D%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=11a-\left[-7m-\left\{6x-4m+2a-6x\right\}\right]")
![=11a-[-7m+4m-2a]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D11a-%5B-7m%2B4m-2a%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=11a-[-7m+4m-2a]")
xv)
xvi)
![\hspace{5pt} m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-\left(m^2-\overline{a^2-2}\right)\right\}\right]-{(m}^2-3a^2-2)](https://s0.wp.com/latex.php?latex=%C2%A0+%5Chspace%7B5pt%7D+%C2%A0+m%5E2-%5Cleft%5B3a%5E2%2B2m%5E2-%5Cleft%5C%7B-3m%5E2%2B2a%5E2-%5Cleft%28m%5E2-%5Coverline%7Ba%5E2-2%7D%5Cright%29%5Cright%5C%7D%5Cright%5D-%7B%28m%7D%5E2-3a%5E2-2%29+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "\hspace{5pt} m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-\left(m^2-\overline{a^2-2}\right)\right\}\right]-{(m}^2-3a^2-2)")
![=m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-\left(m^2-a^2+2\right)\right\}\right]-(m^2-3a^2-2)](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3Dm%5E2-%5Cleft%5B3a%5E2%2B2m%5E2-%5Cleft%5C%7B-3m%5E2%2B2a%5E2-%5Cleft%28m%5E2-a%5E2%2B2%5Cright%29%5Cright%5C%7D%5Cright%5D-%28m%5E2-3a%5E2-2%29+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-\left(m^2-a^2+2\right)\right\}\right]-(m^2-3a^2-2)")
![=m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-m^2+a^2-2\right\}\right]-(m^2-{3a}^2-2)](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3Dm%5E2-%5Cleft%5B3a%5E2%2B2m%5E2-%5Cleft%5C%7B-3m%5E2%2B2a%5E2-m%5E2%2Ba%5E2-2%5Cright%5C%7D%5Cright%5D-%28m%5E2-%7B3a%7D%5E2-2%29+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-m^2+a^2-2\right\}\right]-(m^2-{3a}^2-2)")
![=m^2-\left[3a^2+2m^2-\left\{-4m^2+3a^2-2\right\}\right]-(m^2-{3a}^2-2)](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3Dm%5E2-%5Cleft%5B3a%5E2%2B2m%5E2-%5Cleft%5C%7B-4m%5E2%2B3a%5E2-2%5Cright%5C%7D%5Cright%5D-%28m%5E2-%7B3a%7D%5E2-2%29+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=m^2-\left[3a^2+2m^2-\left\{-4m^2+3a^2-2\right\}\right]-(m^2-{3a}^2-2)")
![=m^2-\left[3a^2+2m^2+4m^2-3a^2+2\right]-(m^2-{3a}^2-2)](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3Dm%5E2-%5Cleft%5B3a%5E2%2B2m%5E2%2B4m%5E2-3a%5E2%2B2%5Cright%5D-%28m%5E2-%7B3a%7D%5E2-2%29+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=m^2-\left[3a^2+2m^2+4m^2-3a^2+2\right]-(m^2-{3a}^2-2)")
![=m^2-\left[6m^2+2\right]-(m^2-{3a}^2-2)](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3Dm%5E2-%5Cleft%5B6m%5E2%2B2%5Cright%5D-%28m%5E2-%7B3a%7D%5E2-2%29+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=m^2-\left[6m^2+2\right]-(m^2-{3a}^2-2)")
xvii)
![\hspace{5pt} 5\left(3-6m\right)-5\left[m-3\left\{2-4\left(m-5\right)\right\}\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%5Chspace%7B5pt%7D+%C2%A0+5%5Cleft%283-6m%5Cright%29-5%5Cleft%5Bm-3%5Cleft%5C%7B2-4%5Cleft%28m-5%5Cright%29%5Cright%5C%7D%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "\hspace{5pt} 5\left(3-6m\right)-5\left[m-3\left\{2-4\left(m-5\right)\right\}\right]")
![=5\left(3-6m\right)-5\left[m-3\left(22-4m\right)\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D5%5Cleft%283-6m%5Cright%29-5%5Cleft%5Bm-3%5Cleft%2822-4m%5Cright%29%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=5\left(3-6m\right)-5\left[m-3\left(22-4m\right)\right]")
![=5\left(3-6m\right)-5\left[13m-66\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D5%5Cleft%283-6m%5Cright%29-5%5Cleft%5B13m-66%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=5\left(3-6m\right)-5\left[13m-66\right]")
xviii)
![\hspace{5pt} q^2-2\left[p^2+pq-\left(p^2+q^2\right)\right]-\left[p^2-2\left\{3pq-\overline{q^2-p^2}\right\}\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%5Chspace%7B5pt%7D+%C2%A0+q%5E2-2%5Cleft%5Bp%5E2%2Bpq-%5Cleft%28p%5E2%2Bq%5E2%5Cright%29%5Cright%5D-%5Cleft%5Bp%5E2-2%5Cleft%5C%7B3pq-%5Coverline%7Bq%5E2-p%5E2%7D%5Cright%5C%7D%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "\hspace{5pt} q^2-2\left[p^2+pq-\left(p^2+q^2\right)\right]-\left[p^2-2\left\{3pq-\overline{q^2-p^2}\right\}\right]")
![=q^2-2\left[p^2+pq-\left(p^2+q^2\right)\right]-\left[p^2-2\left\{3pq-q^2+p^2\right\}\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3Dq%5E2-2%5Cleft%5Bp%5E2%2Bpq-%5Cleft%28p%5E2%2Bq%5E2%5Cright%29%5Cright%5D-%5Cleft%5Bp%5E2-2%5Cleft%5C%7B3pq-q%5E2%2Bp%5E2%5Cright%5C%7D%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=q^2-2\left[p^2+pq-\left(p^2+q^2\right)\right]-\left[p^2-2\left\{3pq-q^2+p^2\right\}\right]")
![=q^2-2\left[pq-q^2]-[p^2-6pq+2q^2-2p^2\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3Dq%5E2-2%5Cleft%5Bpq-q%5E2%5D-%5Bp%5E2-6pq%2B2q%5E2-2p%5E2%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=q^2-2\left[pq-q^2]-[p^2-6pq+2q^2-2p^2\right]")
xix)
![\hspace{5pt} 2\left[3x-\left\{5y-\overline{3x-2y+5}\right\}\right]-2\left(-x-\overline{y-2x}+5\right)](https://s0.wp.com/latex.php?latex=%C2%A0+%5Chspace%7B5pt%7D+%C2%A0+2%5Cleft%5B3x-%5Cleft%5C%7B5y-%5Coverline%7B3x-2y%2B5%7D%5Cright%5C%7D%5Cright%5D-2%5Cleft%28-x-%5Coverline%7By-2x%7D%2B5%5Cright%29+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "\hspace{5pt} 2\left[3x-\left\{5y-\overline{3x-2y+5}\right\}\right]-2\left(-x-\overline{y-2x}+5\right)")
![=2[3x-\left\{\left[5y-3x+2y-5\right\}\right]-2(-x-y+2x+5)](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D2%5B3x-%5Cleft%5C%7B%5Cleft%5B5y-3x%2B2y-5%5Cright%5C%7D%5Cright%5D-2%28-x-y%2B2x%2B5%29+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=2[3x-\left\{\left[5y-3x+2y-5\right\}\right]-2(-x-y+2x+5)")
![=2\left[3x-\left\{7y-3x-5\right\}\right]-2\left(x-y+5\right)](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D2%5Cleft%5B3x-%5Cleft%5C%7B7y-3x-5%5Cright%5C%7D%5Cright%5D-2%5Cleft%28x-y%2B5%5Cright%29+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=2\left[3x-\left\{7y-3x-5\right\}\right]-2\left(x-y+5\right)")
![=2\left[6x-7y+5\right]-2\left(x-y+5\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D2%5Cleft%5B6x-7y%2B5%5Cright%5D-2%5Cleft%28x-y%2B5%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=2\left[6x-7y+5\right]-2\left(x-y+5\right]")
xx)
![\hspace{5pt} -3\left(z+b\right)+13\left(y-c\right)-3\left[c+b+z-2\left\{b+z-3\left(y+c\right)\right\}\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%5Chspace%7B5pt%7D+%C2%A0+-3%5Cleft%28z%2Bb%5Cright%29%2B13%5Cleft%28y-c%5Cright%29-3%5Cleft%5Bc%2Bb%2Bz-2%5Cleft%5C%7Bb%2Bz-3%5Cleft%28y%2Bc%5Cright%29%5Cright%5C%7D%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "\hspace{5pt} -3\left(z+b\right)+13\left(y-c\right)-3\left[c+b+z-2\left\{b+z-3\left(y+c\right)\right\}\right]")
![=-3\left(z+b\right)+13\left(y-c\right)-3\left[c+b+z-2b-2z+6y+6c\right]](https://s0.wp.com/latex.php?latex=%C2%A0+%C2%A0+%3D-3%5Cleft%28z%2Bb%5Cright%29%2B13%5Cleft%28y-c%5Cright%29-3%5Cleft%5Bc%2Bb%2Bz-2b-2z%2B6y%2B6c%5Cright%5D+%C2%A0+%C2%A0+&bg=%23ffffff&fg=%23111111&s=0 "=-3\left(z+b\right)+13\left(y-c\right)-3\left[c+b+z-2b-2z+6y+6c\right]")
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Exercise 16E, Fundamental Concepts and Operations on Algebraic Expressions, ICSE Class 8
Class 8: Fundamental Concepts and Operations on Algebraic Expressions – Exercise 16E
