Question

Thực hiện phép tính

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

Answer 1

(x²-1)(x²+x+1)(x²-x+1)

=(x²-1)[(x²+1)²-x²]

=(x²-1)[x⁴+2x²+1-x²]

=(x²-1)(x⁴+x²+1)

=(x²)³-1

=x⁶-1

Answer 2

( x² - 1 )( x² + x + 1 )( x² - x + 1 )

= ( x² - 1 )[ ( x² + 1 ) + x ][ ( x² + 1 ) - x ]

= ( x² - 1 )[ ( x² + 1 )² - x² ]

= ( x² - 1 )( x⁴ + 2x² + 1 - x² )

= ( x² - 1 )( x⁴ + x² + 1 )

= x⁶ + x⁴ + x² - x⁴ - x² - 1

= x⁶ - 1 

Answer 3

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

Answer 4

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

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

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

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

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

\(=\left(x^2\right)^3-1^3\) 

\(=x^6-1\)

Answer 5

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

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

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

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

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

\(=x^6-1\)