\(2x-1^3+8\)
\(=2x-9\)
\(=\left(\sqrt{2x}\right)^2-3^2\)
\(=\left(\sqrt{2x}-3\right)\left(\sqrt{2x}+3\right)\)
_________
\(8x^3-12x^2+6x-1\)
\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2-1^3\)
\(=\left(2x-1\right)^3\)
_______________
\(8x^3-12x^2+6x-2\)
\(=8x^3-12x^2+6x-1-1\)
\(=\left(2x-1\right)^3-1\)
\(=\left(2x-1-1\right)\left(4x^2-4x+1+2x-1+1\right)\)
\(=\left(2x-2\right)\left(4x^2-2x+1\right)\)
\(=2\left(x-1\right)\left(4x^2-2x+1\right)\)
________
\(9x^3-12x^2+6x-1\)
\(=x^3+8x^3-12x^2+6x-1\)
\(=x^3+\left(2x-1\right)^3\)
\(=\left(x+2x-1\right)\left(x^2-2x^2-x+4x^2-4x+1\right)\)
\(=\left(3x-1\right)\left(3x^2-5x+1\right)\)
b: 8x^3-12x^2+6x-1
=(2x)^3-3*(2x)^2*1+3*2x*1^2-1^3
=(2x-1)^3
c: =(8x^3-12x^2+6x-1)-1
=(2x-1)^3-1
=(2x-1-1)[(2x-1)^2+2x-1+1]
=2(x-1)(4x^2-4x+1+2x)
=2(x-1)(4x^2-2x+1)
8x³ - 12x² + 6x - 1
= (2x)³ - 3.(2x)².1 + 3.2x.1 - 1³
= (2x - 1)³
--------------------
8x³ - 12x² + 6x - 2
= 8x³ - 12x² + 6x - 1 - 1
= (2x)³ - 3.(2x)².1 + 3.(2x).1 - 1³ - 1³
= (2x - 1)³ - 1³
= (2x - 1 - 1)[(2x - 1)² + (2x - 1).1 + 1]
= (2x - 2)(4x² - 4x + 1 + 2x - 1 + 1)
= 2(x - 1)(4x² - 2x + 1)
--------------------
9x³ - 12x² + 6x - 1
= x³ + 8x³ - 12x² + 6x - 1
= x³ + (2x)³ - 3.(2x)² + 3.2x.1² - 1³
= x³ + (2x - 1)³
= (x + 2x - 1)[x² - x.(2x - 1) + (2x - 1)²]
= (3x - 1)(x² - 2x² + x + 4x² - 4x + 1)
= (3x - 1)(3x² - 3x + 1)