Question

因式分解 要过程！

①（m²+n²）²-4m²n²②x²+2x+1-y²③（x²-2）²-（x²-2）-2

Answer 1

①（m²+n²）²-4m²n²
=(m²+n²+2mn)(m²+n²-2mn)
=(m+n)²(m-n)²

②x²+2x+1-y²
=(x+1)²-y²
=(x+1+y)(x+1-y)

③（x²-2）²-（x²-2）-2
=(x²-2-2)(x²-2+1)
=(x+2)(x-2)(x+1)(x-1)

Answer 2

①（m²+n²）²-4m²n²
= (m²+n²-2mn) (m²+n²+2mn)
= (m-n)² (m+n)²

②x²+2x+1-y²
= (x+1)²-y²
=(x+y+1)(x-y+1)

③（x²-2）²-（x²-2）-2
=(x²-2-2) (x²-2+1)
= (x²-4) (x²-1)
=(x+2)(x-2)(x+1)(x-1)