完全平方公式1.197^22.98^23.[x+3]^2-x^24.y^2-[x+y]^25.[a+3][a-3]-[a-1][a+4]6.[xy+1]^2-[xy-1]^2

Question

完全平方公式
1.197^2
2.98^2
3.[x+3]^2-x^2
4.y^2-[x+y]^2
5.[a+3][a-3]-[a-1][a+4]
6.[xy+1]^2-[xy-1]^2

Answer 1

1.197^2
=(200-3)^2
=200^2-2*200*3+3^2
=40000-1200+9
=38809
2.98^2
=(100-2)^2
=100^2-2*100*2+2^2
=10000-400+4
=9604
3.
原式=(x+3+x)(x+3-x)
=3(2x+3)
=6x+9
4.
原式=(y+x+y)(y-x-y)
=-x(x+2y)
=-x^2-2xy
5.
原式=(a^2-9)-(a^2+3a-4)
=a^2-9-a^2-3a+4
=-3a-5
6.
原式=[(xy+1)+(xy-1)][(xy+1)+(xy-1)]
=(xy+1+xy-1)(xy+1-xy+1)
=(2xy+2)*2
=4xy+4