Question

Rút gọn : 

a) ( 4x^2 + y^2 )( 2x + y )( 2x - y ) 

b) ( x + 1 )( x - 2 )( x^2 + 1)( x + 2 )( x - 1 )( x^2 + 4 )

Answer 1

a) ( 4x^2 + y^2 )( 2x + y )( 2x - y ) 

=(4x²+y²)(4x²-y²)

=16x⁴-y⁴

b) ( x + 1 )( x - 2 )( x^2 + 1)( x + 2 )( x - 1 )( x^2 + 4 )

=(x+1)(x-1)(x-2)(x+2)(x²+1)(x²+4)

=(x²-1)(x²-4)(x²+1)(x²+4)

=(x²-1)(x²+1)(x²-4)(x²+4)

=(x⁴-1)(x⁴-16)

=x⁸-17x⁴+16

 

 

 

Answer 2

a) \(\left(4x^2+y^2\right)\left(4x^2-y^2\right)\left(2x+y\right)\left(2x-y\right)\\ =\left(4x^2+y^2\right)\left(4x^2-y^2\right)\\ =16x^4-y^4\)

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

\(=\left(x^2-1\right)\left(x^2+1\right)\left(x^2-4\right)\left(x^2+4\right)\\ =\left(x^4-1\right)\left(x^4-16\right)\\ =x^8-17x+16\)