因式分解 4(a^2-2a+6)(2a^2-a+4)-(3a^2-3a+10) ^2

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因式分解 4(a^2-2a+6)(2a^2-a+4)-(3a^2-3a+10) ^2
因式分解 4(a^2-2a+6)(2a^2-a+4)-(3a^2-3a+10) ^2

因式分解 4(a^2-2a+6)(2a^2-a+4)-(3a^2-3a+10) ^2
设A=a^2-2a+6 B=2a^2-a+4
则A+B=3a^2-3a+10
∴4AB-(A+B)²
=4AB-A²-2AB-B²
=-(A-B)²
=-(a^2-2a+6-2a^2+a-4)²
=-(-a²-a+2)²
=-(a²+a-2)²
=-(a+2)²(a-1)²

4( a" - 2a + 6 )( 2a" - a + 4 ) - ( 3a" - 3a + 10 )"
= 4( a" - 2a + 6 )( 2a" - a + 4 ) - [ ( a" - 2a + 6 ) + ( 2a" - a + 4 ) ]"
= 4( a" - 2a + 6 )( 2a" - a + 4 ) - ( a" - 2a + 6 )" - ( 2a" - a...

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4( a" - 2a + 6 )( 2a" - a + 4 ) - ( 3a" - 3a + 10 )"
= 4( a" - 2a + 6 )( 2a" - a + 4 ) - [ ( a" - 2a + 6 ) + ( 2a" - a + 4 ) ]"
= 4( a" - 2a + 6 )( 2a" - a + 4 ) - ( a" - 2a + 6 )" - ( 2a" - a + 4 )" - 2( a" - 2a + 6 )( 2a - a + 4 )
= 2( a" - 2a + 6 )( 2a" - a + 4 ) - ( a" - 2a + 6 )" - ( 2a" - a + 4 )"
= - [ ( 2a" - a + 4 ) - ( a" - 2a + 6 ) ]"
= - [ 2a" - a + 4 - a" + 2a - 6 ]"
= - [ a" + 2a - a - 2 ]"
= - [ a( a + 2 ) - ( a + 2 ) ]"
= - [ ( a + 2 )( a - 1 ) ]"
= - ( a + 2 )"( a - 1 )"

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