\displaystyle \text{Simplify each of the following algebraic expressions:}

\displaystyle \textbf{Question 1: }9z+5z\times2-3z\div3
\displaystyle \text{Answer:}
\displaystyle 9z+5z\times2-3z\div3
\displaystyle =9z+10z-z=18z.
\displaystyle \\

\displaystyle \textbf{Question 2: }42c\div14\times3-10c\div5+c
\displaystyle \text{Answer:}
\displaystyle 42c\div14\times3-10c\div5+c
\displaystyle =3c\times3-2c+c
\displaystyle =9c-2c+c=8c.
\displaystyle \\

\displaystyle \textbf{Question 3: }20y+4y\div2-\frac{1}{3}\times9y
\displaystyle \text{Answer:}
\displaystyle 20y+4y\div2-\frac{1}{3}\times9y
\displaystyle =20y+2y-3y=19y.
\displaystyle \\

\displaystyle \textbf{Question 4: }10m-4m\times3+8m\div4
\displaystyle \text{Answer:}
\displaystyle 10m-4m\times3+8m\div4
\displaystyle =10m-12m+2m=0.
\displaystyle \\

\displaystyle \textbf{Question 5: }16a-8ax\div4x+\frac{1}{2}\times6a
\displaystyle \text{Answer:}
\displaystyle 16a-8ax\div4x+\frac{1}{2}\times6a
\displaystyle =16a-2a+3a=17a.
\displaystyle \\

\displaystyle \textbf{Question 6: }15n-12n\div4+6n\times2- 6n\div\left(\frac{1}{2}\text{ of }4\right)
\displaystyle \text{Answer:}
\displaystyle 15n-12n\div4+6n\times2- 6n\div\left(\frac{1}{2}\text{ of }4\right)
\displaystyle =15n-12n\div4+6n\times2-6n\div2
\displaystyle =15n-3n+12n-3n=21n.
\displaystyle \\

\displaystyle \textbf{Question 7: }9.6a\div0.32\times2+ 4.5a\div(0.5\text{ of }3)-2a
\displaystyle \text{Answer:}
\displaystyle 9.6a\div0.32\times2+4.5a\div(0.5\text{ of }3)-2a
\displaystyle =9.6a\div0.32\times2+4.5a\div1.5-2a
\displaystyle =30a\times2+3a-2a
\displaystyle =60a+3a-2a=61a.
\displaystyle \\

\displaystyle \textbf{Question 8: }6x\times(0.3\text{ of }2.5)\div0.25
\displaystyle \text{Answer:}
\displaystyle 6x\times(0.3\text{ of }2.5)\div0.25
\displaystyle =6x\times(0.3\times2.5)\div0.25
\displaystyle =6x\times0.75\div0.25
\displaystyle =6x\times3=18x.
\displaystyle \\

\displaystyle \textbf{Question 9: }2(8x+3x\times2)- 4(5x\times2\div4)
\displaystyle \text{Answer:}
\displaystyle 2(8x+3x\times2)-4(5x\times2\div4)
\displaystyle =2(8x+6x)-4\left(\frac{5x}{2}\right)
\displaystyle =2(14x)-10x
\displaystyle =28x-10x=18x.
\displaystyle \\

\displaystyle \textbf{Question 10: }5a- [2b-\{2a-4(a-2b)-3(b-\overline{2a-b})\}]
\displaystyle \text{Answer:}
\displaystyle 5a-[2b-\{2a-4(a-2b)-3(b-\overline{2a-b})\}]
\displaystyle =5a-[2b-\{2a-4(a-2b)-3(b-2a+b)\}]
\displaystyle =5a-[2b-\{2a-4a+8b-6b+6a\}]
\displaystyle =5a-[2b-\{4a+2b\}]
\displaystyle =5a-[2b-4a-2b]
\displaystyle =5a-(-4a)=9a.
\displaystyle \\

\displaystyle \textbf{Question 11: }4t-(2p+2t)-(-5p+3t)
\displaystyle \text{Answer:}
\displaystyle 4t-(2p+2t)-(-5p+3t)
\displaystyle =4t-2p-2t+5p-3t
\displaystyle =3p-t.
\displaystyle \\

\displaystyle \textbf{Question 12: }x-y+z-(x+z-y)-(y+z-x)-(x+y+x)
\displaystyle \text{Answer:}
\displaystyle x-y+z-(x+z-y)-(y+z-x)-(x+y+x)
\displaystyle =x-y+z-x-z+y-y-z+x-x-y-x
\displaystyle =-x-2y-z.
\displaystyle \\

\displaystyle \textbf{Question 13: }2y-x\{3y-(2-2y)\}-3x(1-4y)
\displaystyle \text{Answer:}
\displaystyle 2y-x\{3y-(2-2y)\}-3x(1-4y)
\displaystyle =2y-x\{3y-2+2y\}-3x(1-4y)
\displaystyle =2y-x(5y-2)-3x(1-4y)
\displaystyle =2y-5xy+2x-3x+12xy
\displaystyle =-x+2y+7xy.
\displaystyle \\

\displaystyle \textbf{Question 14: }11a- [-7m-\{6x-(4m-\overline{2a-6x})\}]
\displaystyle \text{Answer:}
\displaystyle 11a-[-7m-\{6x-(4m-\overline{2a-6x})\}]
\displaystyle =11a-[-7m-\{6x-(4m-2a+6x)\}]
\displaystyle =11a-[-7m-\{6x-4m+2a-6x\}]
\displaystyle =11a-[-7m-\{-4m+2a\}]
\displaystyle =11a-[-7m+4m-2a]
\displaystyle =11a+7m-4m+2a
\displaystyle =13a+3m.
\displaystyle \\

\displaystyle \textbf{Question 15: }16xy^2\div4x+ \frac{3}{4x^2}\times8x^2y^2-(2x-\overline{7y+2x})\times xy
\displaystyle \text{Answer:}
\displaystyle 16xy^2\div4x+\frac{3}{4x^2}\times8x^2y^2 -(2x-\overline{7y+2x})\times xy
\displaystyle =4y^2+6y^2-\{2x-(7y+2x)\}xy
\displaystyle =4y^2+6y^2-\{2x-7y-2x\}xy
\displaystyle =4y^2+6y^2-(-7y)xy
\displaystyle =10y^2+7xy^2
\displaystyle =y^2(10+7x).
\displaystyle \\

\displaystyle \textbf{Question 16: }m^2- \left[3a^2+2m^2-\left\{-3m^2+2a^2- \left(m^2-\overline{a^2-2}\right)\right\}\right]
\displaystyle -(m^2-3a^2-2)
\displaystyle \text{Answer:}
\displaystyle m^2-\left[3a^2+2m^2- \left\{-3m^2+2a^2-\left(m^2-\overline{a^2-2}\right)\right\}\right]
\displaystyle -(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]
\displaystyle -(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]
\displaystyle -(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-(6m^2+2)-(m^2-3a^2-2)
\displaystyle =m^2-6m^2-2-m^2+3a^2+2
\displaystyle =-6m^2+3a^2.
\displaystyle \\

\displaystyle \textbf{Question 17: }5(3-6m)- 5\left[m-3\left\{2-4(m-5)\right\}\right]
\displaystyle \text{Answer:}
\displaystyle 5(3-6m)-5\left[m-3\left\{2-4(m-5)\right\}\right]
\displaystyle =5(3-6m)-5\left[m-3(22-4m)\right]
\displaystyle =5(3-6m)-5(13m-66)
\displaystyle =15-30m-65m+330
\displaystyle =-95m+345.
\displaystyle \\

\displaystyle \textbf{Question 18: }q^2- 2\left[p^2+pq-(p^2+q^2)\right]
\displaystyle -\left[p^2- 2\left\{3pq-\overline{q^2-p^2}\right\}\right]
\displaystyle \text{Answer:}
\displaystyle q^2-2\left[p^2+pq-(p^2+q^2)\right]- \left[p^2-2\left\{3pq-\overline{q^2-p^2}\right\}\right]
\displaystyle =q^2-2\left[p^2+pq-(p^2+q^2)\right]- \left[p^2-2\left\{3pq-q^2+p^2\right\}\right]
\displaystyle =q^2-2(pq-q^2)- \left[p^2-6pq+2q^2-2p^2\right]
\displaystyle =q^2-2pq+2q^2+p^2+6pq-2q^2
\displaystyle =p^2+4pq+q^2.
\displaystyle \\

\displaystyle \textbf{Question 19: }2\left[3x- \left\{5y-\overline{3x-2y+5}\right\}\right]
\displaystyle -2\left(-x-\overline{y-2x}+5\right)
\displaystyle \text{Answer:}
\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-3x+2y-5\right\}\right] -2(-x-y+2x+5)
\displaystyle =2\left[3x-\left\{7y-3x-5\right\}\right] -2(x-y+5)
\displaystyle =2(6x-7y+5)-2(x-y+5)
\displaystyle =12x-14y+10-2x+2y-10
\displaystyle =10x-12y.
\displaystyle \\

\displaystyle \textbf{Question 20: }-3(z+b)+13(y-c)- 3\left[c+b+z-2\left\{b+z-3(y+c)\right\}\right]
\displaystyle \text{Answer:}
\displaystyle -3(z+b)+13(y-c)- 3\left[c+b+z-2\left\{b+z-3(y+c)\right\}\right]
\displaystyle =-3(z+b)+13(y-c)- 3[c+b+z-2b-2z+6y+6c]
\displaystyle =-3(z+b)+13(y-c)-3(7c-b-z+6y)
\displaystyle =-3z-3b+13y-13c-21c+3b+3z-18y
\displaystyle =-5y-34c.
\displaystyle \\

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