a) `65^2-35^2`
`=(65-35)(65+35)`
`=30.100`
`=30000`
Áp dụng:
`A^2-B^2=(A-B)(A+B)`
b) `65^2-35^2+83^2-17^2`
`=(65^2-35^2)+(83^2-17^2)`
`=(65-35)(65+35)+(83-17)(83+17)`
`=30.100+66.100`
`=100.(30+66)`
`=100.96`
`=9600`
Áp dụng:
`A^2-B^2=(A-B)(A+B)`
c) `35^2+40.35+20^2-45^2`
`=(35^2+2.35.20+20^2)-45^2`
`=(35+20)^2-45^2`
`=(35+20-45)(35+20+45)`
`=10.100`
`=1000`
Áp dụng:
`(A+B)^2=A^2+2AB+B^2`
`A^2-B^2=(A-B)(A+B)`
d) `(83^2-17^2)/(51,5^2-48,5^2)`
`=((83-17)(83+17))/((51,5-48,5)(51,5+48,5))`
`=(66.100)/(3.100)`
`=22`
Áp dụng:
`A^2-B^2=(A-B)(A+B)`