12x³ + 4x² - 27x - 9

= 4x² ( 3x + 1 ) - 9 ( 3x + 1 )

= ( 3x +1 ) ( 4x² -9 )

k nha !

      \(12x^3+4x^2-27x-9\)

\(=4x^2\left(3x+1\right)-9\left(3x+1\right)\)

\(=\left(3x+1\right)\left(4x^2-9\right)\)

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

Chúc bạn học tốt.

     \(4x\left(x-1\right)=8\left(x+1\right)\)

\(\Rightarrow4x^2-4x=8x+8\)

\(\Rightarrow4x^2-4x-8x-8=0\)

\(\Rightarrow4x^2-12x-8=0\)

\(\Rightarrow\left(2x\right)^2-2.2x.3+9-17=0\)

\(\Rightarrow\left(2x-3\right)^2=17\)

\(\Rightarrow\orbr{\begin{cases}2x-3=\sqrt{17}\\2x-3=-\sqrt{17}\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{\sqrt{17}+3}{2}\\x=\frac{-\sqrt{17}+3}{2}\end{cases}}}\)

Chúc bạn học tốt.

Easy \(x^2-n^2-2xy+y^2-m^2+2mn\)

\(=\left(x^2-2xy+y^2\right)-\left(n^2-2mn+m^2\right)\)

\(=\left(x-y\right)^2-\left(n-m\right)^2\)

\(=\left(x-y-n+m\right)\left(x-y+n-m\right)\)

\(x^2-n^2-2xy+y^2-m^2+2mn\)

\(=\left(x^2-2xy+y^2\right)-\left(n^2-2mn+m^2\right)\)

\(=\left(x-y\right)^2-\left(n-m\right)^2\)

\(=\left(x-y-n+m\right)\left(x-y+n-m\right)\)

       \(a^2-10a+25-y^2-4yz-4z^2\)

\(=a^2-2.a.5+5^2-y^2-2.y.2z-\left(2z\right)^2\)

\(=\left(a-5\right)^2-\left(y+2z\right)^2\)

\(=\left(a-y-2z-5\right)\left(a+y+2z-5\right)\)

Very easy

\(a^2-10a+25-y^2-4yz-4z^2\)

\(=\left(a-5\right)^2-\left(y+2z\right)^2\)

\(=\left(a-5-y-2z\right)\left(a-5+y+2z\right)\)

       \(3a^2c^2+bd+3abc+acd\)

\(=\left(3a^2c^2+3abc\right)+\left(acd+bd\right)\)

\(=3ac\left(ac+b\right)+d\left(ac+b\right)\)

\(=\left(ac+b\right)\left(3ac+d\right)\)

     \(-16x^2+8xy-y^2+49\)

\(=49-\left(16x^2-8xy+y^2\right)\)

\(=7^2-\left(4x-y\right)^2\)

\(=\left(7-4x+y\right)\left(7+4x-y\right)\)

      \(x^6-x^4+2x^3+2x^2\)

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

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

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

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

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