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會用到
(a+b)=a^2+2*a*b+b^2
(a-b)=a^2-2*a*b+b^2
(a+b)*(a-b)=a^2-b^2

1.計算1000.5^2

(1000+0.5)^2
=1000^2+2*1000*0.5+0.5^2
=1000000+1000+0.25
=1001000.25

2.如果520^2=500^2+A, 則A的值和?

(500+20)^2=500^2+2*500*20+20^2
A=20400

3.計算157^2+314*43+43^2=?

157^2+314*43+43^2
=157^2+2*157*43+43^2
=(157+43)^2
=200^2
=40000

4.計算:32.8^2-65.6*2.8+2.8^2=?

32.8^2-65.6*2.8+2.8^2
=32.8^2-2*32.8*2.8+2.8^2
=(32.8-2.8)^2
=30^2
=900

5.求解996^2的過成為1000^2+a*4+4^2,則a=?

996^2
=(1000-4)^2
=1000^2-2*1000*4+4^2
a=-2000

6.試求最接近499.5^2的整數為何?

(500-0.5)^2
=250000-500+0.25
=249500.25
最接近的整數為249500

7. 408*398=? (這題你有抄錯嗎?)

408*(400-2)
=163200-816
=162384

8. 197^2-203^2=?

197^2-203^2
=(197+203)*(197-203)
=400*(-6)
=-2400

9.503*497=500^2-a^2=b 則a=? b=?

503*497
=(500+3)*(500-3)
=500^2-3^2
=249991 a=3 b=249991

10.求1987*2013-1997^2=?

(2000-13)*(2000+13)-1997^2
=2000^2-13^2-1997^2
=(2000+1997)*(2000-1997)-169
=3997*3-169
=11991-169
=11822

有看不懂的可再發問

參考資料 自己辛苦算的

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