\(c,=\left(100-7\right)\left(100+7\right)=10000-49=9951\\ d,=127^2+2\cdot73\cdot127+73^2=\left(127+73\right)^2=200^2=40000\)

c) 93.107 = (100 - 7)(100 + 7)

= 100^2 - 7^2 = 10000 - 49 

= 9951

d) 127^2 + 146.127 + 73^2

= (127 + 73)^2

= 200^2 = 40000

a) \(=\left(127+73\right)^2=200^2=40000\)

b) \(=18^8-\left(18^8-1\right)=1\)

c) \(=\left(100+99\right)\left(100-99\right)+\left(98+97\right)\left(98-97\right)+...+\left(2+1\right)\left(2-1\right)\)

\(=100+99+98+97+...+2+1=5050\)

d) biến đổi thành \(20^2-19^2+18^2-17^2+..+2^2-1^2\)

rồi giải ra như trên

\(13-32+51-70+89-108+127-146+165\)

\(=\left(13+127\right)-\left(32+108\right)+\left(51+89\right)-\left(70+146-165\right)\)

\(=140-140+140-51\)

\(=140-51\)

\(=89\)

Mong mn giúp mình nhanh nha mik đang cần rất gấp gáp đó chiều nay mik đi học thêm rồi

13 - 32

= 13 - ( 30 + 2 )

= (13 + 2 ) + 30

= 15 + 30

= 45

Answer:

\(A=127^2+146.127+73^2\)

\(=127^2+2.127.73+73^2\)

\(=\left(127+73\right)^2\)

\(=200^2\)

\(=40000\)

\(B=9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)\)

\(=\left(9.2\right)^8-[\left(18^4\right)^2-1]\)

\(=18^8-18^8+1\)

\(=1\)

\(C=\left(20^2+18^2+16^2+...+4^2+2^2\right)-\left(19^2+17^2+15^2+...+3^2+1^2\right)\)

\(=20^2+18^2+16^2+...+4^2+2^2-19^2-17^2-15^2-...-3^2-1^2\)

\(=\left(20^2-19^2\right)+\left(18^2-17^2\right)+...+\left(2^2-1^2\right)\)

\(=\left(20-19\right)\left(20+19\right)+\left(18-17\right)\left(18+17\right)+...+\left(2-1\right)+\left(2+1\right)\)

\(=1.39+1.35+...+1.3\)

\(=39+35+...+3\)

Số số hạng \(\frac{39-3}{4}+1=10\) số hạng

Tổng \(\frac{\left(39+3\right).10}{2}=210\)

 a,  \(C=127^2+146.127+73^2\)

         \(=127^2+2.127.73+73^2\)

         \(=\left(127+73\right)^2\)

         \(=200^2=40000\)

a, \(\frac{2006^3+1}{2006^2-2005}\)

\(=\frac{\left(2006+1\right)\left(2006^2-2006+1\right)}{2006^2-2005}=\frac{2007\left(2006^2-2005\right)}{2006^2-2005}=2007\)

     \(\frac{2006^3-1}{2006^2+2007}\)

\(=\frac{\left(2006-1\right)\left(2006^2+2006+1\right)}{2006^2+2007}=\frac{2005\left(2006^2+2007\right)}{2006^2+2007}=2005\)

Chúc bạn học tốt.

a) 127² + 146.127 + 73²

= 127² + 2.73.127 + 73²

= (127 + 73)² = 200² = 40000

b) 9⁸ . 2⁸ - (18⁴ - 1)(18⁴ + 1)

= (9.2)⁸ - 18⁸ + 1

= 18⁸ - 18⁸ + 1 = 1

c) \(\frac{780^2-220^2}{125^2+150.125+75^2}=\frac{\left(780-220\right)\left(780+220\right)}{125^2+2.75.125+75^2}=\frac{560.1000}{\left(125+75\right)^2}=\frac{560000}{200^2}\)

\(=\frac{560000}{40000}=14\)

a) 127² + 146.127 + 73²

= 127² + 2.73.127 + 73²

= ( 127 + 73 )²

= 200² = 40 000

b) 9⁸.2⁸ - ( 18⁴ - 1 )( 18⁴ + 1 ) 

= ( 9.2 )⁸ - [ ( 18⁴ )² - 1² ]

= 18⁸ - 18⁸ + 1

= 1

c) \(\frac{780^2-220^2}{125^2+150\cdot125+75^2}\)

\(=\frac{\left(780-220\right)\left(780+220\right)}{125^2+2\cdot75\cdot125+75^2}\)

\(=\frac{560\cdot1000}{\left(125+75\right)^2}\)

\(=\frac{560000}{200^2}\)

\(=\frac{560000}{40000}=14\)

             Bài làm :

a) 127² + 146.127 + 73²

= 127² + 2.73.127 + 73²

= ( 127 + 73 )²

= 200² 

= 40 000

b) 9⁸.2⁸ - ( 18⁴ - 1 )( 18⁴ + 1 ) 

= ( 9.2 )⁸ - [ ( 18⁴ )² - 1² ]

= 18⁸ - 18⁸ + 1

= 1

 \(\text{c)}\frac{780^2-220^2}{125^2+150\cdot125+75^2}\)

\(=\frac{\left(780-220\right)\left(780+220\right)}{125^2+2\cdot75\cdot125+75^2}\)

\(=\frac{560\cdot1000}{\left(125+75\right)^2}\)

\(=\frac{560000}{200^2}\)

\(=\frac{560000}{40000}\)

\(=14\)

a/ \(127^2+146\cdot127+73^2=127^2+2\cdot73\cdot127+73^2=\left(127+73\right)^2=200^2=40000\)

b/ \(100^2-99^2+98^2-97^2+...+2^2-1^2=\left(100^2-99^2\right)+\left(98^2-97^2\right)+...+\left(2^2-1^2\right)\)

\(=100+99+98+97+...+2+1=\frac{\left(100\right)\left(100+1\right)}{2}=5050\)

c/ \(34^2+66^2+68\cdot66=34^2+66^2+2\cdot34\cdot66=\left(34+66\right)^2=100^2=10000\)