Question

几道数学题，很快，需解答

平方差公式计算，需过程
9.8*10.2
25又1/5*24又4/5
100^2-99^2+98^2-97^2+96^2-95^2+……+2^2-1^2

分解因式，需过程
2a^3-8a
x^4-16
(a+b)^2-4b^2
1/2x^4y^2-1/8x^2y^4
9x^2-16(a+b)^2
(x+y)^3(x-y)-(x+y)(x-y)^3
25(x-2y)^3+4(2y-x)
81a^5b^5-ab

Answer 1

9.8*10.2
=(10-0.2)(10+0.2)
=100-0.04
=99.96

25又1/5*24又4/5
=(25+1/5)(25-1/5)
=25^2-(1/5)^2
=625-0.04
=624.96

100^2-99^2+98^2-97^2+96^2-95^2+……+2^2-1^2
=(100+99)(100-99)+(98+97)(98-97).....+(2+1)(2-1)
=199+195+191+......+3
=(199+3)*(199-3)/2
=202*98
=19796

2a^3-8a
=2a(a^2-4)
=2a(a+2)(a-2)

x^4-16
=x^4-4^2
=(x^2+4)(x^2-4)
=(x^2+4)(x+2)(x-2)

(a+b)^2-4b^2
=(a+b+2b)(a+b-2b)
=(a+3b)(a-b)

1/2x^4y^2-1/8x^2y^4
=1/2x^2y^2(x^2-1/4y^2)
=1/2x^2y^2(x+1/2y)(x-1/2y)

9x^2-16(a+b)^2
=(3x)^2-[4(a+b)]^2
=[3x-4(a+b)][3x+4(a+b)]
=(3x-4a-4b)(3x+4a+4b)

(x+y)^3(x-y)-(x+y)(x-y)^3
=(x+y)(x-y)[(x+y)^2-(x-y)^2]
=(x+y)(x-y)(x+y+x-y)(x+y-x+y)
=(x+y)(x-y)*2x*2y
=4xy(x+y)(x-y)

25(x-2y)^3+4(2y-x)
=(x-2y)[25(x-2y)^2-4]
=(x-2y)[(5(x-2y)+2][5(x-2y)-2]

81a^5b^5-ab
=ab[81a^4b^4-1]
=ab[(3ab)^4-1]
=ab[(3ab)^2+1][(3ab)^2-1]
=ab[(3ab)^2+1][(3ab+1)(3ab-1)]