\(1.\left(x-2\right)\left(x-1\right)=x\left(2x+1\right)+2\)

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

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

\(\Leftrightarrow-x^2-4x=0\)

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

\(\Leftrightarrow\orbr{\begin{cases}x=0\\-x-4=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-4\end{cases}}\)Vậy S={-4;0}

\(2.\left(x+2\right)\left(x+2\right)-\left(x-2\right)\left(x-2\right)=8x\)

\(\Leftrightarrow\left(x+2\right)^2-\left(x-2\right)^2-8x=0\)

\(\Leftrightarrow x^2+4x+4-\left(x^2-4x+4\right)-8x=0\)

\(\Leftrightarrow x^2+4x+4-x^2+4x-4-8x=0\)

\(\Leftrightarrow0=0\)(luôn đúng vs mọi giá trị của x)

\(3.\left(2x-1\right)\left(x^3-x+1\right)=2x^3-3x^2+16=0\)

\(\Leftrightarrow2x^4-2x^2+2x-x^3+x-1=2x^3-3x^2+16=0\)

\(\Leftrightarrow2x^4-x^3-2x^2+3x-1=2x^3-3x^2+16=0\)

\(\Leftrightarrow2x^4-x^3-2x^3-2x^2+3x^2+3x-1-16=0\)

\(\Leftrightarrow2x^4-3x^3+x^2+3x-17=0\)

Cái này là phương trình bậc 4 lận, Giải hơi mất thời gian

a: \(x^4-2x^3+x^2-2x\)

\(=\left(x^4-2x^3\right)+\left(x^2-2x\right)\)

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

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

b: \(x^4+x^3-8x-8\)

\(=\left(x^4+x^3\right)-\left(8x+8\right)\)

\(=x^3\left(x+1\right)-8\left(x+1\right)\)

\(=\left(x+1\right)\left(x^3-8\right)\)

\(=\left(x+1\right)\left(x-2\right)\left(x^2+2x+4\right)\)

\(a,P=\left(x^2+8x\right)\left(2x-5\right)+x^2\left(-11-2x\right)-8+40x\)

\(=2x^3-5x^2+16x^2-40x-11x^2-2x^3-8+40x\)

\(=\left(2x^3-2x^3\right)+\left(-5x^2+16x^2-11x^2\right)+\left(-40x+40x\right)-8\)

\(=-8\)

\(\Rightarrow \) Giá trị của \(P\) không phụ thuộc vào biến \(x\).

\(b,Q=\left(5x-2\right)\left(x^2+2x\right)-x\left(5x^2+8x-4\right)+26\)

\(=5x^3+10x^2-2x^2-4x-5x^3-8x^2+4x+26\)

\(=\left(5x^3-5x^3\right)+\left(10x^2-2x^2-8x^2\right)+\left(-4x+4x\right)+26\)

\(=26\)

\(\Rightarrow\) Giá trị của \(Q\) không phụ thuộc vào biến \(x\).

\(c,B=3x\left(x+5\right)-\left(3x+18\right)\left(x-1\right)+14\)

\(=3x^2+15x-\left(3x^2-3x+18x-18\right)+14\)

\(=3x^2+15x-3x^2+3x-18x+18+14\)

\(=\left(3x^2-3x^2\right)+\left(15x+3x-18x\right)+\left(18+14\right)\)

\(=32\)

\(\Rightarrow\) Giá trị của \(B\) không phụ thuộc vào biến \(x\).

#\(Toru\)

a: =2x^3-5x^2+16x^2-40x-11x^2-2x^3-8+40x

=-8

b: =5x^3+10x^2-2x^2-4x-5x^3-8x^2+4x+26

=26

c: =3x^2+15x-3x^2+3x-18x+18+14

=32

\(8x^3+\left(x+8\right)^2=8\left(x+2\right)\left(x^2-2x+4\right)\)

\(8x^3+x^2+2\times x\times8+8^2=8\left(x^3+2^3\right)\)

\(8x^3+x^2+16x+64+8x^2=8\left(x^3+8\right)\)

\(8x^3+x\times\left(x+16\right)+64=8x^3+64\)

\(8x^3-8x^3+64-64+x\times\left(x+16\right)=0\)

\(x\times\left(x+16\right)=0\)

TH1:

\(x=0\)

TH2:

\(x+16=0\)

\(x=-16\)

Vậy x = 0 hoặc x = -16

\(8x^3+\left(x+8\right)^2=8\left(x+2\right)\left(x^2-2x+4\right)\)

\(\Leftrightarrow8x^3+x^2+16x+64=8\left(x^3+8\right)\)

\(\Leftrightarrow8x^3+x^2+16x+64=8x^3+64\)

\(\Leftrightarrow8x^3+x^2+16x+64-8x^3-64=0\)

\(\Leftrightarrow x^2+16x=0\)

\(\Leftrightarrow x\left(x+16\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x+16=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=-16\end{array}\right.\)

\(8x^3+\left(x+8\right)^2=8\left(x+2\right)\left(x^2-2x+4\right)\)
\(\Leftrightarrow8x^3+\left(x^2+16x+61\right)=8\left(x^3+2^3\right)\)
\(\Leftrightarrow8x^3+x^2+16x+61=8x^3+61\)
\(\Leftrightarrow8x^3+x^2+16x+61-8x^3-61=0\)
\(\Leftrightarrow x^2+16x=0\)
\(\Leftrightarrow x\left(x+16\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x+16=0\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=0\\x=-16\end{array}\right.\)
\(\text{Vậy x=0 hoặc x=-16 }\)

\(\Leftrightarrow-2x+1-x-2=8\cdot\left(-4x^2+6x-2x\right)+4\left(x^2-2x+1\right)=0\)

\(\Leftrightarrow-3x-1+32x^2-48x+16x-4x^2+8x-4=0\)

\(\Leftrightarrow28x^2-27x-5=0\)

\(\text{Δ}=\left(-27\right)^2-4\cdot28\cdot\left(-5\right)=1289>0\)

Do đó: Phương trình có hai nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x_1=\dfrac{27-\sqrt{1289}}{56}\\x_2=\dfrac{27+\sqrt{1289}}{56}\end{matrix}\right.\)