Question

利用因式分解计算(要写过程）

99*101*10001

49(a-b)^2-16(a+b)^2

2x^2-1/2y^2

Answer 1

99*101*10001
=(100-1)(100+1)*10001
=(100^2-1)*10001
=(100^2-1)(100^2+1)
=100^4-1
=99999999

49(a-b)^2-16(a+b)^2
=[7(a-b)+4(a+b)][7(a-b)-4(a+b)]
=(11a-3b)(3a-11b)

2x^2-1/2y^2
=2(x^2-1/4y^2 )
=2(x+1/2y)(x-1/2y)

Answer 2

99*101*1001=（100-1）*（100+1）*10001=(100^2-1^2)*10001=9999*10001=(10000-1)*(10000+1)=10000^2-1^2=99999999

49(a-b)^2-16(a+b)^2 ={7(a-b)}^2-{4(a+b)}^2=（7a-7b+4a+4b）(7a-7b-4a-4b)=(11a-3b)(3a-11b)

2x^2-1/2y^2=1/2{（2x)^2-y^2}=1/2(2x+y)(2x-y)