Simplify each of the following algebraic expression:

Question 1: $\displaystyle 9z+5z \times 2-3z \div 3$

$\displaystyle 9z+5z \times 2-3z \div 3 =9z+10z-z =18z$

$\displaystyle \\$

Question 2: $\displaystyle 42c \div 14 \times 3-10c \div 5+c$

$\displaystyle 42c \div 14 \times 3-10c \div 5+c =3c \times 3-2c+c =9c-2c+c=8c$

$\displaystyle \\$

Question 3: $\displaystyle 20y+4y \div 2- \frac{1}{3} \times 9y$

$\displaystyle 20y+4y \div 2- \frac{1}{3} \times 9y =20y+2y-3y =19y$

$\displaystyle \\$

Question 4: $\displaystyle 10m-4m \times 3+8m \div 4$

$\displaystyle 10m-4m \times 3+8m \div 4 =10m-12m+2m=0$

$\displaystyle \\$

Question 5: $\displaystyle 16a-8ax \div 4x+ \frac{1}{2} \times 6a$

$\displaystyle 16a-8ax \div 4x+ \frac{1}{2} \times 6a =16a-2a+3a =17a$

$\displaystyle \\$

Question 6: $\displaystyle 15n-12n \div 4+6n \times 2-6n \div \frac{1}{2} \ of\ 4$

$\displaystyle 15n-12n \div 4+6n \times 2-6n \div \frac{1}{2} \ of\ 4 =15n-3n+12n-3n =21n$

$\displaystyle \\$

Question 7: $\displaystyle 9.6a \div 0.32 \times 2+4.5a \div 0.5\ of\ 3-2a$

$\displaystyle 9.6a \div 0.32 \times 2+4.5a \div 0.5\ of\ 3-2a$

$\displaystyle =9.6a \div 0.32 \times 2+4.5a \div 1.5-2a =60a+3a-2a=61a$

$\displaystyle \\$

Question 8: $\displaystyle 6x \times 0.3\ of\ 2.5 \div 0.25$

$\displaystyle 6x \times 0.3\ of\ 2.5 \div 0.25 =6x \times \left(0.3 \times 2.5\right) \div 0.25 =6x \times \frac{0.75}{0.25} =18x$

$\displaystyle \\$

Question 9: $\displaystyle 2\left(8x+3x \times 2\right)-4\left(5x \times 2 \div 4\right)$

$\displaystyle 2\left(8x+3x \times 2\right)-4\left(5x \times 2 \div 4\right) =2\left(8x+6x\right)-4( \frac{5x}{2} ) =28x-10x=18x$

$\displaystyle \\$

Question 10: $\displaystyle 5a-[2b-\{2a-4\left(a-2b\right)-3\left(b-\overline{2a-b})\right\}]$

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

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

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

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

$\displaystyle \\$

Question 11: $\displaystyle 4t-(2p+2t)-(-5p+3t)$

$\displaystyle 4t-(2p+2t)-(-5p+3t)$

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

$\displaystyle =3p-t$

$\displaystyle \\$

Question 12: $\displaystyle x-y+z-\left(x+z-y\right)-\left(y+z-x\right)-\left(x+y+x\right)$

$\displaystyle x-y+z-\left(x+z-y\right)-\left(y+z-x\right)-\left(x+y+x\right)$

$\displaystyle =x-y+z-x-z+y-y-z+x-x-y-z$

$\displaystyle =-2y-2z$

$\displaystyle \\$

Question 13: $\displaystyle 2y-x\left\{3y-\left(2-2y\right)\right\}-3x\left(1-4y\right)$

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

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

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

$\displaystyle =-x+2y+7xy$

$\displaystyle \\$

Question 14: $\displaystyle 11a-\left[-7m-\left\{6x-\left(4m-\overline{2a-6x}\right)\right\}\right]$

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

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

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

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

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

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

$\displaystyle \\$

Question 15: $\displaystyle 16xy^2 \div 4x+ \frac{3}{4x^2} \times 8x^2y^2-(2x-\overline{7y+2x}) \times xy$

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

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

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

$\displaystyle \\$

Question 16: $\displaystyle m^2-\left[3a^2+2m^2-\left\{-3m^2+2a^2-\left(m^2-\overline{a^2-2}\right)\right\}\right]-{(m}^2-3a^2-2)$

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

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

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

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

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

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

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

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

$\displaystyle \\$

Question 17: $\displaystyle 5\left(3-6m\right)-5\left[m-3\left\{2-4\left(m-5\right)\right\}\right]$

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

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

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

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

$\displaystyle =-95m+345$

$\displaystyle \\$

Question 18: $\displaystyle q^2-2\left[p^2+pq-\left(p^2+q^2\right)\right]-\left[p^2-2\left\{3pq-\overline{q^2-p^2}\right\}\right]$

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

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

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

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

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

$\displaystyle \\$

Question 19: $\displaystyle 2\left[3x-\left\{5y-\overline{3x-2y+5}\right\}\right]-2\left(-x-\overline{y-2x}+5\right)$

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

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

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

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

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

$\displaystyle =10x-12y$

$\displaystyle \\$

Question 20: $\displaystyle -3\left(z+b\right)+13\left(y-c\right)-3\left[c+b+z-2\left\{b+z-3\left(y+c\right)\right\}\right]$

$\displaystyle -3\left(z+b\right)+13\left(y-c\right)-3\left[c+b+z-2\left\{b+z-3\left(y+c\right)\right\}\right]$
$\displaystyle =-3\left(z+b\right)+13\left(y-c\right)-3\left[c+b+z-2b-2z+6y+6c\right]$
$\displaystyle =-3\left(z+b\right)+13\left(y-c\right)-3\left(7c-b-z+6y\right)$
$\displaystyle =-3z-3b+13y-13c-21c+3b+3z-18y$
$\displaystyle =-5y-34c$