Question

几道数学题·初二 从第三题往下一定要写过程，快没分了%>_<%

1.（mn-1)² -(mn-1)(mn+1)2.(x+y/2)² +(x-y/2)² 3. a^4-(a-b)(a+b)(a² -b² )
5.(x-1)² +(y+2)² -(x+y)(x-y) 6.97×99×101×103=？（用乘法公式）
还剩5分！！！！！！

Answer 1

解：1.（mn-1)² -(mn-1)(mn+1)
=（mn-1)（mn-1-mn-1)
=1-mn
2.(x+y/2)² +(x-y/2)²
=(x+y/2)²+(x-y/2)(x+y/2)
=(x+y/2)(x+y/2+x-y/2)
=(x+y/2)2x
=2x²+xy
=x(2x+y)

3. a^4-(a-b)(a+b)(a² -b² )
=a^4-(a² -b² ))(a² -b² )
=a^4- [(a² -b² )]²
=(a²)²-[(a² -b² )]²
=(a²+a² -b² ) (a²-a² +b² )
=(2a² -b² )b²
=2a²b² -b^4

4..(x-1)² +(y+2)² -(x+y)(x-y)
=x²-2x+1+y²+4y+4-(x²-y²)
=4y-2x+2y²+5
=2y(y+2)-2x+5

5..97×99×101×103
=(100-3)×(1oo-1)×(100+1)×(100+3)
=(100²-3²)(100²-1²)
=(10000-9)(10000-1)
=10000²-10000-90000+9
=10000²-100000+9
=100000000-100000+9
=99900009

Answer 2

1.（mn-1)² -(mn-1)(mn+1)
＝(mn-1)[mn-1-(mn+1)]
＝-2(mn-1)

2.(x+y/2)² +(x-y/2)²
＝2x² +y² /2

3. a^4-(a-b)(a+b)(a² -b²)
＝a^4 -(a² -b²)²
＝(a²+a²-b²)(a²-a²+b²)
=b²(2a²+b²)
=2a²b²+b^4

5.(x-1)² +(y+2)² -(x+y)(x-y)
＝(x-1)² +(y+2)² -x²+y²
＝x²-2x+1+y²+2y+4-x²+y²
＝2y²+2y-2x+5

6.97×99×101×103
＝(100-3)×(100+3)×(100-1)×(100+1)
＝（100²-9）×(100²-1)
＝100^4-10×100²+9
＝100000000-100000+9
＝99900009

Answer 3

-m²n²-2mn+3 2x²+2xy+y²/2
a^4-(a-b)(a+b)(a² -b² )= a^4-(a²-b²)²=2a²b²-b^4
(x-1)² +(y+2)² -(x+y)(x-y) =4y-2x+5+2y²
97×99×101×103=（100-3)(100+3)(100-1)(100+1)