Question

初二数学题，从3题往下，写过程！！

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）

Answer 1

1.（mn-1)² -(mn-1)(mn+1)
=(mn-1)(mn-1-mn-1)
=2-2mn
2.(x+y/2)² +(x-y/2)²
=(x+y/2+x-y/2)^2-2(x+y/2)(x-y/2)
=4x^2-2x^2+y^2/2
=2x^2+y^2/2
3. a^4-(a-b)(a+b)(a² -b² )
=a^4-(a^2-b^2)^2
=a^4-a^4+2a^2b^2-b^4
=2b^2(a+b)(a-b)
5.(x-1)² +(y+2)² -(x+y)(x-y)
=x^2-2x+1+y^2+4y+4-x^2+y^2
=2y^2+4y-2x+5
6.97×99×101×103
=(100-3)(100-1)(100+1)(100+3)
=(100^2-3^2)(100^2-1^2)
=(10000-9)(10000-1)
=10000^2-(9+1)*10000+9
=100000000-100000+9
=99900009

Answer 2

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

2.(x+y/2)² +(x-y/2)²
=x^2+xy+y^2/4 +x^2-xy+y^2/4
=2x^2+y^2/2
3.a^4-(a-b)(a+b)(a² -b² )
= a^4-(a² -b²)(a² -b² )
=a^4-( a² -b²)^2
=a^4-(a^4-2a^2b^2+b^4)
=2a^2b^2- b^4

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

6. 97×99×101×103
=(100-3)(100+3)(100-1)(100+1)
=100^2-9+100^2-1
=19990