15 \(\times\) ( 2\(x\) - 16) - (6\(x^2\) + 15\(x\)): 3\(x\) = 20

15 \(\times\) (2\(x\) - 16) - 3\(x\)( 2\(x\) +  5):3\(x\) = 20

30\(x\) - 240 - (2\(x\) + 5) = 20

30\(x\) - 240 - 2\(x\) - 5 = 20

28\(x\) - 245 = 20

28\(x\)           = 20 + 245

28\(x\)          = 265

     \(x\)         = 265:28

15(2x-16)-(6\(x^2\)+15x):3x=20

=>30x-240-2x-5=20

=>28x=265

=>x=\(\dfrac{265}{28}\)

f: Ta có: \(x\left(2x-9\right)-4x+18=0\)

\(\Leftrightarrow\left(2x-9\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=2\end{matrix}\right.\)

g: Ta có: \(4x\left(x-1000\right)-x+1000=0\)

\(\Leftrightarrow\left(x-1000\right)\left(4x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1000\\x=\dfrac{1}{4}\end{matrix}\right.\)

f. x(2x - 9) - 4x + 18 = 0

<=> x(2x - 9) - 2(2x - 9) = 0

<=> (x - 2)(2x - 9) = 0

<=> \(\left[{}\begin{matrix}x-2=0\\2x-9=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=2\\x=\dfrac{9}{2}\end{matrix}\right.\)

g. 4x(x - 1000) - x + 1000 = 0

<=> 4x(x - 1000) - (x - 1000) = 0

<=> (4x - 1)(x - 1000) = 0

<=> \(\left[{}\begin{matrix}4x-1=0\\x-1000=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=1000\end{matrix}\right.\)

h. 2x(x - 4) - 6x²(-x + 4) = 0

<=> 2x(x - 4) + 6x²(x - 4) = 0

<=> (2x + 6x²)(x - 4) = 0

<=> 2x(1 + 3x)(x - 4) = 0

<=> \(\left[{}\begin{matrix}2x=0\\1+3x=0\\x-4=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=0\\x=\dfrac{-1}{3}\\x=4\end{matrix}\right.\)

i. 2x(x - 3) + x² - 9 = 0

<=> 2x(x - 3) + (x - 3)(x + 3) = 0

<=> (2x + x + 3)(x - 3) = 0

<=> (3x + 3)(x + 3) = 0

<=> \(\left[{}\begin{matrix}3x+3=0\\x+3=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=-1\\x=-3\end{matrix}\right.\)

j. 9x - 6x² + x³ = 0

<=> x(9 - 6x + x²) = 0

<=> x(3 - x)² = 0

<=> \(\left[{}\begin{matrix}x=0\\3-x=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)

 4x(x – 1000) – x + 1000 = 0

(4x-1)(x-1000)                 =0

⇔x=1/4 hoặc  1000

\(=12x^3-10x+18x^2-15\)

\(\left(6x^3-7x^2-x+2\right):\left(2x+1\right)\\ =\left[\left(6x^3-6x^2\right)-\left(x^2-x\right)-\left(2x-2\right)\right]:\left(2x+1\right)\\ =\left[\left(x-1\right)\left(6x^2-x-2\right)\right]:\left(2x+1\right)\\ =\left\{\left(x-1\right)\left[\left(6x^2+3x\right)-\left(4x+2\right)\right]\right\}:\left(2x+1\right)\\ =\left[\left(x-1\right)\left(3x-2\right)\left(2x+1\right)\right]:\left(2x+1\right)\\ =\left(x-1\right)\left(3x-2\right)\)

\(\left(6x^2-5\right)\left(2x+3\right)=2x\left(6x^2-5\right)+3\left(6x^2-5\right)=12x^3-10x+18x^2-15\)

c: \(\left(2x+3\right)^2+\left(2x-3\right)^2-\left(2x+3\right)\left(2x-3\right)\)

\(=4x^2+12x+9+4x^2-12x+9-\left(4x^2-9\right)\)

\(=8x^2+18-4x^2+9=4x^2+27\)

d: \(\left(x-1\right)\cdot\left(x^2+x+1\right)-\left(2x+3\right)\left(4x^2-6x+9\right)\)

\(=\left(x-1\right)\left(x^2+x\cdot1+1^2\right)-\left(2x+3\right)\left[\left(2x\right)^2-2x\cdot3+3^2\right]\)

\(=x^3-1-8x^3-27=-7x^3-28\)

e: \(\left(x+1\right)^3-\left(x-1\right)^3-6x^2\)

\(=x^3+3x^2+3x+1-6x^2-\left(x^3-3x^2+3x-1\right)\)

\(=x^3-3x^2+3x+1-x^3+3x^2-3x+1\)

=2

a: (1-2x)^3-(1+2x)^3

\(=1^3-3\cdot1^2\cdot2x+3\cdot1\cdot\left(2x\right)^2-8x^3-8x^3-12x^2-6x-1\)

\(=1-6x+12x^2-8x^3-8x^3-12x^2-6x-1\)

\(=-16x^3-12x\)

b: \(=x^3-6x^2+12x-8-x^3-x^2+8\)

\(=-7x^2+12x\)

c: \(=x^3+8-12x+6x^2-x^3+6x^2+12x\)

\(=12x^2+8\)

1) \(\left(\dfrac{1}{2}x+3\right)\left(x^2-4x-6\right)\)

\(=\dfrac{1}{2}x^3-2x^2-3x+3x^2-12x-18\)

\(=\dfrac{1}{2}x^3+x^2-15x-18\)

2) \(\left(6x^2-9x+15\right)\left(\dfrac{2}{3}x+1\right)\)

\(=4x^3+6x^2-6x^2-9x+10x+15\)

\(=4x^3+x+15\)

3) Ta có: \(\left(3x^2-x+5\right)\left(x^3+5x-1\right)\)

\(=3x^5+15x^2-3x^2-x^4-5x^2+x+5x^3+25x-5\)

\(=3x^5-x^4+5x^3+10x^2+26x-5\)

4) Ta có: \(\left(x-1\right)\left(x+1\right)\left(x-2\right)\)

\(=\left(x^2-1\right)\left(x-2\right)\)

\(=x^3-2x^2-x+2\)

\(6x^2-2x\left(3x+\dfrac{3}{2}\right)=9\)

\(\Rightarrow6x^2-6x^2-3x=9\)

\(\Rightarrow-3x=9\)

\(\Rightarrow x=\dfrac{9}{-3}\)

\(\Rightarrow x=-3\)

\(6x^2-2x\left(3x+\dfrac{3}{2}\right)=9\\ \Leftrightarrow6x^2-6x^2-3x=9\\ \Leftrightarrow3x=9\\ \Leftrightarrow x=3\)

\(6x^2-2x\left(3x+\dfrac{3}{2}\right)=9\\ \Rightarrow6x^2-\left(6x^2+3x\right)=9\\ \Rightarrow6x^2-6x^2-3x=9\\ \Rightarrow-3x=9\\ \Rightarrow x=9:-3\\ \Rightarrow x=-3\)

Câu 6:Thực hiện phép nhân  -2x(x² + 3x - 4) ta được:

A.-2x³ - 6x² – 8x          B. 2x³ -6x² – 8x      C. -2x³ - 6x² + 8x         D. -2x³ + 3x² -4

Câu 7 : Phân tích đa thức x² + 2xy + y² – 9z² thành nhân tử ta được:

A. (x+y+3z)(x+y–3z)  

B. (x-y+3z)(x+y–3z) 

C.(x - y +3z)(x - y – 3z)

D. (x + y +3z)(x -y – 3z)

Câu 9: Phân tích đa thức x² + 7x + 12 thành nhân tử ta được:

A. (x - 3)( x + 4 )         B. (x + 3)( x + 4 )         C.(x + 5)( x + 2 )               D. (x -5)( x + 2 )

Câu 10:  Giá trị của biểu thức  (x² + 4x + 4) tại x = - 2 là:

A. 4                            B. -2                          C. 0                           D. -8

Mấy câu còn lại bị lỗi r nhé

Câu 6:C

Câu 7:A

Câu 9:B

Câu 10:A