Question

数学因式分解 ⑴9（x-y）²-25 ⑵（x²-y）²-（2y-2）² ⑶（a²-2b）²-（1-2b

Answer 1

⑴9（x-y）2-25=（3x-3y+5)(3x-3y-5)
⑵（x2-y）2-（2y-2）2=(x2-y+2y-2)(x2-y-2y+2)=(x2+y-2)(x2-3y+2)
⑶（a2-2b）2-（1-2b)2=(a2-2b+1-2b)(a2-2b-1+2b)=(a2-4b+1)(a2-1)=(a2-4b+1)(a-1)(a+1)

Answer 2

⑴ 9（x-y）²-25
=[3(x-y)+5][3(x-y)-5]
=[3x-3y+5][3x-3y-5]
⑵（x²-y）²-（2y-2）²
=(x^2-y+2y-2)(x^2-y-2y+2)
=(x^2+y-2)(x^2-3y+2)
⑶（a²-2b）²-（1-2b）²
=(a^2-2b+1-2b)(a^2-2b-1+2b)
=(a^2-4b+1)(a+1)(a-1)