Question

请将多项式(a+2)(a+6)+4因式分解 若取a=x的平方-4x，则原式变成了

Answer 1

( a + 2 )( a + 6 ) + 4
= ( a + 4 - 2 )( a + 4 + 2 ) + 4
= ( a + 4 )” - 2” + 2”
= ( a + 4 )”

( x” - 4x + 2 )( x” - 4x + 6 ) + 4
= ( x” - 4x + 4 - 2 )( x” - 4x + 4 + 2 ) + 4
= [ ( x - 2 )” - 2 ][ ( x - 2 )” + 2 ] + 4
= ( x - 2 )^4 - 2” + 2”
= ( x - 2 )^4

Answer 2

(a+2)(a+6)+4
=a²+2a+6a+2×6+4
=a²+8a+16
=(a+4)²
当a=x²-4x,则
原式=(x²-4x+4)²
=(x-2)^4