Đáp án:

$\begin{array}{l}
8)\\
a)A = \left( {x + 3} \right)\left( {{x^2} - 3x + 9} \right) - \left( {54 + {x^3}} \right)\\
 = {x^3} + 27 - 54 - {x^3}\\
 =  - 27\\
b)B = \left( {2x + y} \right)\left( {4{x^2} - 2xy + {y^2}} \right)\\
 - \left( {2x - y} \right)\left( {4{x^2} + 2xy + {y^2}} \right)\\
 = {\left( {2x} \right)^3} + {y^3} - {\left( {2x} \right)^3} + {y^3}\\
 = 2{y^3}\\
c)C = {\left( {a + b} \right)^2} - {\left( {a - b} \right)^2}\\
 = \left( {a + b - a + b} \right)\left( {a + b + a - b} \right)\\
 = 2b.2a\\
 = 4ab\\
d)D = {\left( {a + b} \right)^3} - {\left( {a - b} \right)^3} - 2{b^3}\\
 = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}\\
 - {a^3} + 3{a^2}b - 3a{b^2} + {b^3} - 2{b^3}\\
 = 6{a^2}b\\
e)E = {\left( {x + y + z} \right)^2} - 2\left( {x + y + z} \right)\left( {x + y} \right) + {\left( {x + y} \right)^2}\\
 = {\left( {x + y + z - x - y} \right)^2}\\
 = {z^2}\\
9)\\
a){\left( {2x + 1} \right)^2} - 4{\left( {x + 2} \right)^2} = 9\\
 \Leftrightarrow 4{x^2} + 4x + 1 - 4{x^2} - 16x - 16 = 9\\
 \Leftrightarrow 12x =  - 24\\
 \Leftrightarrow x =  - 2\\
Vậy\,x =  - 2\\
b)3{\left( {x - 1} \right)^2} - 3x\left( {x - 5} \right) = 21\\
 \Leftrightarrow 3{x^2} - 6x + 3 - 3{x^2} + 15x = 21\\
 \Leftrightarrow 9x = 18\\
 \Leftrightarrow x = 2\\
Vậy\,x = 2\\
c){\left( {x + 3} \right)^2} - \left( {x - 4} \right)\left( {x + 8} \right) = 1\\
 \Leftrightarrow {x^2} + 6x + 9 - {x^2} - 4x + 32 = 1\\
 \Leftrightarrow 2x =  - 40\\
 \Leftrightarrow x =  - 20\\
Vậy\,x =  - 20\\
d)3{\left( {x + 2} \right)^2} + {\left( {2x - 1} \right)^2} - 7\left( {x + 3} \right)\left( {x - 3} \right) = 36\\
 \Leftrightarrow 3{x^2} + 12x + 12 + 4{x^2} - 4x + 1\\
 - 7\left( {{x^2} - 9} \right) = 36\\
 \Leftrightarrow 7{x^2} + 8x + 13 - 7{x^2} + 63 = 36\\
 \Leftrightarrow 8x =  - 40\\
 \Leftrightarrow x =  - 5\\
Vậy\,x =  - 5\\
e)\left( {x - 1} \right)\left( {{x^2} + x + 1} \right) - x\left( {x + 2} \right)\left( {x - 2} \right) = 5\\
 \Leftrightarrow {x^3} - 1 - x\left( {{x^2} - 4} \right) = 5\\
 \Leftrightarrow {x^3} - 1 - {x^3} + 4x = 5\\
 \Leftrightarrow 4x = 6\\
 \Leftrightarrow x = \dfrac{3}{2}\\
Vậy\,x = \dfrac{3}{2}
\end{array}$

`8.`

`a)A=(x+3)(x^2-3x+9)-(54+x^3)`

`=x^3+27-54-x^3`

`=(x^3-x^3)+(27-54)`

`=-27`

`b)B=(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)`

`=8x^3+y^3-(8x^3-y^3)`

`=8x^3+y^3-8x^3+y^3`

`=(8x^3-8x^3)+(y^3+y^3)`

`=2y^3`

`c)C=(a+b)^2-(a-b)^2`

`=[(a+b)+(a-b)][(a+b)-(a-b)]`

`=(a+b+a-b)(a+b-a+b)`

`=2a.2b`

`=4ab`

`d)D=(a+b)^3-(a-b)^3-2b^3`

`=a^3+3a^2b+3ab^2+b^3-(a^3-3a^2b+3ab^2-b^3)-2b^3`

`=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-2b^3`

`=(a^3-a^3)+(3a^2b+3a^2b)+(3ab^2-3ab^2)+(b^3+b^3-2b^3)`

`=6a^2b`

`e)E=(x+y+z)^2-2(x+y+z)(x+y)+(x+y)^2`

`=[(x+y+z)-(x+y)]^2`

`=(x+y+z-x-y)^2`

`=z^2`

`9.`

`a)(2x+1)^2-4(x+2)^2=9`

`⇔4x²+4x+1-4(x²+4x+4)=9`

`⇔4x²+4x+1-4x²-16x-16=9`

`⇔(4x²-4x²)+(4x-16x)+(1-16)=9`

`⇔-12x-15=9`

`⇔-12x=9+15`

`⇔-12x=24`

`⇔x=24:(-12)`

`⇔x=-2`

Vậy `x=-2`

`b)3(x-1)^2-3x(x-5)=21`

`⇔3(x²-2x+1)-3x²+15x=21`

`⇔3x²-6x+3-3x²+15x=21`

`⇔(3x²-3x²)+(-6x+15x)+3=21`

`⇔9x+3=21`

`⇔9x=21-3`

`⇔9x=18`

`⇔x=18:9`

`⇔x=2`

Vậy `x=2`

`c)(x+3)^2-(x-4)(x+8)=1`

`⇔x^2+6x+9-(x^2+8x-4x-32)=1`

`⇔x^2+6x+9-x^2-8x+4x+32=1`

`⇔(x^2-x^2)+(6x-8x+4x)+(9+32)=1`

`⇔2x+41=1`

`⇔2x=1-41`

`⇔2x=-40`

`⇔x=(-40):2`

`⇔x=-20`

Vậy `x=-20`

`d)3(x+2)^2+(2x-1)^2-7(x+3)(x-3)=36`

`⇔3(x^2+4x+4)+4x^2-4x+1-7(x^2-9)=36`

`⇔3x^2+12x+12+4x^2-4x+1-7x^2+63=36`

`⇔(3x^2+4x^2-7x^2)+(12x-4x)+(12+1+63)=36`

`⇔8x+76=36`

`⇔8x=36-76`

`⇔8x=-40`

`⇔x=(-40):8`

`⇔x=-5`

Vậy `x=-5`

`e)(x-1)(x^2+x+1)-x(x+2)(x-2)=5`

`⇔x^3-1-x(x^2-4)=5`

`⇔x^3-1-x^3+4x=5`

`⇔4x-1=5`

`⇔4x=5+1`

`⇔4x=6`

`⇔x=6/4`

`⇔x=3/2`

Vậy `x=3/2`