Simplify each of the following algebraic expression:

Question 1:  9z+5z \times 2-3z \div 3

Answer:

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

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

Answer:

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

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

Answer:

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

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

Answer:

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

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

Answer:

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

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

Answer:

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

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

Answer:

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

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

Answer:

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

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

Answer:

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

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

Answer:

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

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Question 11:  4t-(2p+2t)-(-5p+3t)

Answer:

4t-(2p+2t)-(-5p+3t)

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

=3p-t

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

Answer:

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

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

Answer:

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

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

Answer:

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

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

Answer:

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

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Question 16:  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)

Answer:

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

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

Answer:

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

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Question 18:  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]

Answer:

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

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

Answer:

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

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Question 20:  -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]

Answer:

-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