Simplify each of the following algebraic expression:

i) $\hspace{5pt} 9z+5z\times{}2-3z\div{}3$

$=9z+10z-z$

$=18z$

ii) $\hspace{5pt} 42c\div{}14\times{}3-10c\div{}5+c$

$=3c\times{}3-2c+c$

$=9c-2c+c=8c$

iii) $\hspace{5pt} 20y+4y\div{}2-\frac{1}{3}\times 9y$

$=20y+2y-3y =19y$

iv) $\hspace{5pt} 10m-4m\times{}3+8m\div{}4$

$=10m-12m+2m=0$

v) $\hspace{5pt} 16a-8ax\div{}4x+\frac{1}{2}\times{}6a$

$=16a-2a+3a$

$=17a$

vi) $\hspace{5pt} 15n-12n\div{}4+6n\times{}2-6n\div{}\frac{1}{2}of\ 4$

$=15n-3n+12n-3n$

$=21n$

vii) $\hspace{5pt} 9.6a\div{}0.32\times{}2+4.5a\div{}0.5\ of\ 3-2a$

$=9.6a\div{}0.32\times{}2+4.5a\div{}1.5-2a$

$=60a+3a-2a=61a$

viii) $\hspace{5pt} 6x\times{}0.3\ of\ 2.5\div{}0.25$

$=6x\times{}\left(0.3\times{}2.5\right)\div{}0.25$

$=6x\times{}\frac{0.75}{0.25}$

$=18x$

ix) $\hspace{5pt} 2\left(8x+3x\times{}2\right)-4\left(5x\times{}2\div{}4\right)$

$=2\left(8x+6x\right)-4(\frac{5x}{2})$

$=28x-10x=18x$

x) $\hspace{5pt} 5a-[2b-\{2a-4\left(a-2b\right)-3\left(b-\overline{2a-b})\right\}]$

$=5a-\left[2b-\left\{2a-4\left(a-2b\right)-3\left(b-2a+b\right)\right\}\right]$

$=5a-[2b-\left\{2a-4a+8b-6b+6a\right\}]$

$=5a-\left[2b-\left\{4a+2b\right\}\right]=\ 9a$

xi) $\hspace{5pt} 4t-(2p+2t)-(-5p+3t)$

$=4t-2p-2t+5p-3t$

$=3p-t$

xii) $\hspace{5pt} x-y+z-\left(x+z-y\right)-\left(y+z-x\right)-\left(x+y+x\right)$

$=x-y+z-x-z+y-y-z+x-x-y-z$

$=-2y-2z$

xiii) $\hspace{5pt} 2y-x\left\{3y-\left(2-2y\right)\right\}-3x\left(1-4y\right)$

$=2y-x\left\{3y-2+2y\right\}-3x\left(1-4y\right)$

$=2y-5xy+2x-3x+12xy$

$=-x+2y+7xy$

xiv) $\hspace{5pt} 11a-\left[-7m-\left\{6x-\left(4m-\overline{2a-6x}\right)\right\}\right]$

$=11a-\left[-7m-\left\{6x-\left(4m-2a+6x\right)\right\}\right]$

$=11a-[-7m-\left\{6x-4m+2a-6x\right\}$

$=11a-\left[-7m-\left\{6x-4m+2a-6x\right\}\right]$

$=11a-[-7m+4m-2a]$

$=11a+7m-4m+2a=13a+3m$

xv) $\hspace{5pt} 16xy^2\div{}4x+\frac{3}{4x^2}\times{}8x^2y^2-(2x-\overline{7y+2x})\times{}xy$

$=\frac{16xy^2}{4x}+\frac{24\ x^2y^2}{4x^2}-\left(2x-7y-2x\right)y$

$=4y^2+6y^2+7y^2=17y^2$

xvi) $\hspace{5pt} m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-\left(m^2-\overline{a^2-2}\right)\right\}\right]-{(m}^2-3a^2-2)$

$=m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-\left(m^2-a^2+2\right)\right\}\right]-(m^2-3a^2-2)$

$=m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-m^2+a^2-2\right\}\right]-(m^2-{3a}^2-2)$

$=m^2-\left[3a^2+2m^2-\left\{-4m^2+3a^2-2\right\}\right]-(m^2-{3a}^2-2)$

$=m^2-\left[3a^2+2m^2+4m^2-3a^2+2\right]-(m^2-{3a}^2-2)$

$=m^2-\left[6m^2+2\right]-(m^2-{3a}^2-2)$

$=m^2-6m^2-2-m^2+3a^2+2$

$=-{6m}^2+3a^2$

xvii) $\hspace{5pt} 5\left(3-6m\right)-5\left[m-3\left\{2-4\left(m-5\right)\right\}\right]$

$=5\left(3-6m\right)-5\left[m-3\left(22-4m\right)\right]$

$=5\left(3-6m\right)-5\left[13m-66\right]$

$=15-30m-65m+330$

$=-95m+345$

xviii) $\hspace{5pt} q^2-2\left[p^2+pq-\left(p^2+q^2\right)\right]-\left[p^2-2\left\{3pq-\overline{q^2-p^2}\right\}\right]$

$=q^2-2\left[p^2+pq-\left(p^2+q^2\right)\right]-\left[p^2-2\left\{3pq-q^2+p^2\right\}\right]$

$=q^2-2\left[pq-q^2]-[p^2-6pq+2q^2-2p^2\right]$

$=q^2-2pq+2q^2+p^2-2q^2+6pq$

$=q^2+p^2+4pq$

xix) $\hspace{5pt} 2\left[3x-\left\{5y-\overline{3x-2y+5}\right\}\right]-2\left(-x-\overline{y-2x}+5\right)$

$=2[3x-\left\{\left[5y-3x+2y-5\right\}\right]-2(-x-y+2x+5)$

$=2\left[3x-\left\{7y-3x-5\right\}\right]-2\left(x-y+5\right)$

$=2\left[6x-7y+5\right]-2\left(x-y+5\right]$

$=12x-14y+10-2x+2y-10$

$=10x-12y$

xx) $\hspace{5pt} -3\left(z+b\right)+13\left(y-c\right)-3\left[c+b+z-2\left\{b+z-3\left(y+c\right)\right\}\right]$

$=-3\left(z+b\right)+13\left(y-c\right)-3\left[c+b+z-2b-2z+6y+6c\right]$

$=-3\left(z+b\right)+13\left(y-c\right)-3\left(7c-b-z+6y\right)$

$=-3z-3b+13y-13c-21c+3b+3z-18y$

$=-5y-34c$