Question

因式分解：已知a+b=5,ab=3,求(a²-b²)²的值

Answer 1

(a-b)²
=a²+b²-2ab
=(a+b)²-4ab
=5²-4x3
=25-12
=13

(a²-b²)²
=(a+b)²(a-b)²
=25x13
=325

Answer 2

(a-b)^2=(a+b)^2-4ab=25-12=13
(a²-b²)²
=（a+b）^2(a-b)^2
=25*13
=325

Answer 3

(a-b)²(a+b)²＝（a²+b²-4ab+2ab)×25=[(a+b)²-4ab]×25=(25-12)×25=325

Answer 4

（a2-b2）2=（a+b)2*(a-b)2
(a-b)2=(a+b)2-4ab=25-4*3=13
(a2-b2)2=25*13=325

Answer 5

a²－b²＝(a＋b)(a－b)＝±5√13

Answer 6

（a+b)2*(a-b)2 (a-b)2=(a+b)2-4ab=25-4*3=13 (a2-b2)2=25*13=325