Question

几道因式分解题，求解

Answer 1

a"b" - 4ab + 4
= ( ab )" - 4( ab ) + 2"
= ( ab - 2 )"

a^4 - 4b"
= ( a" )" - ( 2b )"
= ( a" - 2b )( a" + 2b )

(1/2)x" - 2xy" + 2(y^4)
= ( 1/2 )[ x" - 4xy" + 4(y^4) ]
= ( 1/2 )[ x" - 2(x)(2y") + ( 2y" )" ]
= ( 1/2 )( x - 2y" )"

-9a" + 12ab - 4b"
= -[ (3a)" - 2(3a)(2b) + (2b)" ]
= - ( 3a - 2b )"

( a - 2b )" - 12( a - 2b ) + 36
= ( a - 2b )" - 12( a - 2b ) + 6"
= ( a - 2b - 6 )"

16(x^4) - ( 4 - 8x )"
= ( 4x" )" - ( 8x - 4 )"
= ( 4x" + 8x - 4 )( 4x" - 8x + 4 )
= 16( x" + 2x - 1 )( x" - 2x + 1 )
= 16( x" + 2x - 1 )( x - 1 )"
如果继续分解，就是
= 16( x" + 2x + 1 - 2 )( x - 1 )"
= 16[ ( x + 1 )" - (√2)" ]( x - 1 )"
= 16( x + 1 + √2 )( x + 1 - √2 )( x - 1 )"