Question

数学因式分解

1、16-（2a+3b）² 2、-36x²+12xy-y² 3、4x（a-b）-8y（b-a） 4、（x²-5）²+8（x²-5）+16

Answer 1

16 - ( 2a + 3b )"
= 4" - ( 2a + 3b )"
= [ 4 - ( 2a + 3b ) ][ 4 + ( 2a + 3b ) ]
= ( 4 - 2a - 3b )( 4 + 2a + 3b )

-36x" + 12xy - y"
= - ( 36x" - 12xy + y" )
= - [ ( 6x )" - 2( 6x )y + y" ]
= - ( 6x - y )"

4x( a - b ) - 8y( b - a )
= 4( a - b )x + 4( 2y )( a - b )
= 4( a - b )( x + 2y )

( x" - 5 )" + 8( x" - 5 ) + 16
= ( x" - 5 )" + 2( x" - 5 )( 4 ) + 4"
= ( x" - 5 + 4 )"
= ( x" - 1 )"
= ( x - 1 )"( x + 1 )"

Answer 2

(1)16-(2a+3b)²
=(4+2a+3b)(4-2a-3b)

(2)-36x²+12xy-y²
=-(36x²-12xy+y²)
=-(6x-y)²

(3)4x(a-b)-8y(b-a)
=4x(a-b)+8y(a-b)
=4(a-b)(x+2y)

4)(x²-5)²+8(x²-5)+16
=(x²-5+4)²
=(x²-1)²
=(x+1)²(x-1)²

追问

(1)16-(2a+3b)²

过程能详细点不？嘿嘿

追答

平方差 4的平方减后面的 能采纳了不？这自己写下