因式分解：（x+1）×（x+2）×（x+3）×（x+4）+1
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原式=[(x+1)(x+4)][(x+2)(x+3)]+1
=[(x²+5x)+4][(x²+5x)+6]+1
=(x²+5x)²+10(x²+5x)+24+1
=(x²+5x)²+10(x²+5x)+25
=(x²+5x+5)²
=[(x²+5x)+4][(x²+5x)+6]+1
=(x²+5x)²+10(x²+5x)+24+1
=(x²+5x)²+10(x²+5x)+25
=(x²+5x+5)²
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( x + 1 )( x + 2 )( x + 3 )( x + 4 ) + 1
= [ ( x + 1 )( x + 4 ) ][ ( x + 2 )( x + 3 ) ] + 1
= ( x" + 4x + x + 4 )( x" + 3x + 2x + 6 ) + 1
= ( x" + 5x + 4 )( x" + 5x + 6 ) + 1
= ( x" + 5x )" + 6( x" + 5x ) + 4( x" + 5x ) + 24 + 1
= ( x" + 5x )" + 10( x" + 5x ) + 25
= ( x" + 5x + 5 )"
= [ ( x + 1 )( x + 4 ) ][ ( x + 2 )( x + 3 ) ] + 1
= ( x" + 4x + x + 4 )( x" + 3x + 2x + 6 ) + 1
= ( x" + 5x + 4 )( x" + 5x + 6 ) + 1
= ( x" + 5x )" + 6( x" + 5x ) + 4( x" + 5x ) + 24 + 1
= ( x" + 5x )" + 10( x" + 5x ) + 25
= ( x" + 5x + 5 )"
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