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    

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