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

\(=\left(x+2\right)\left(5x-1-2x+6\right)-3\left(x^2+4x+4\right)\)

\(=\left(x+2\right)\left(3x+5\right)-3x^2-12x-12=-x-2\)

\(x^2+2x+1-y^2\)

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

\(=\left(x+1-y\right)\left(x+1+y\right)\)

\(2x^3+16\)

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

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

\(B=3\left(x^2-\frac{11}{3}x+5\right)\)

\(=3\left(x^2-\frac{11}{3}x+\frac{121}{36}+\frac{59}{36}\right)=3\left(x-\frac{11}{6}\right)^2+\frac{59}{12}\)

\(\ge\frac{59}{12}\)

12x-5)(4x-1)+(3x-7)(1-16x)=81

⇒48x2−32x+5−48x2+115x−7=81

⇒48x2−32x+5−48x2+115x−7=81

⇒83x=83

⇒x=1

(12x-5)(4x-1)+(3x-7)(1-16x)=81

12x ( 4x- 1) - 5(4x-1) + 3x(1-16x) -7(1-16x) =81

12x . 4x -12x - 20x + 5 + 3x - 3x. 16x - 7 + 7.16x = 81

48x^2 -12x - 20x + 5 + 3x - 48x^2 - 7 + 112x = 81

(48x^2 - 48x^2) + (112x - 12x - 20x +3x) - ( 7 - 5) =81

83x = 81 + 2

83x =83

x=1

x^2 - y^2  + 4 - 4*x

=   - ( y - x + 2 )  *( y + x - 2 )

Phân tích thành nhân tử:
x^2 - y^2 - 4x + 4
=(x^2-4x+4)-y^2
=(x-2)^2-y^2
=(x-2+y)(x-2-y)

x =0

 hình như thế

a) \(f\left(x\right)=2x^3+9x^2-9x+m\)

Để \(f\left(x\right)\)chia hết cho \(2x-1\)thì \(f\left(x\right)=\left(2x-1\right)q\left(x\right)\)(với \(q\left(x\right)\)là đa thức thương)

Khi đó \(f\left(\frac{1}{2}\right)=0\)

Từ đây suy ra \(m=2\).

b) \(f\left(x\right)=2x^4-8x^3+5x^2+mx+n\)

Để \(f\left(x\right)\)chia hết cho \(2x^2-1\)thì \(f\left(x\right)=\left(2x^2-1\right)q\left(x\right)\)(với \(q\left(x\right)\)là đa thức thương)

Có \(2x^2-1=0\Leftrightarrow x=\pm\sqrt{\frac{1}{2}}\).

Suy ra \(f\left(\sqrt{\frac{1}{2}}\right)=f\left(-\sqrt{\frac{1}{2}}\right)=0\)

Từ đây suy ra \(\hept{\begin{cases}\sqrt{\frac{1}{2}}m+n=3-2\sqrt{2}\\-\sqrt{\frac{1}{2}}m+n=3+2\sqrt{2}\end{cases}}\Leftrightarrow\hept{\begin{cases}m=-4\\n=3\end{cases}}\).