\(B=\frac{780^2-220^2}{125^2+150.125+75^2}\)\(=\frac{\left(780+220\right).\left(780-220\right)}{\left(125+75\right)^2}\)\(=\frac{1000.560}{200^2}\)\(=\frac{560000}{40000}=14\)

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

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

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

\(=\left(100+1\right).\frac{100-1}{2}=\frac{101.99}{2}=\frac{9999}{2}\)

Ta có ( 10 a   –   5 ) 2   =   100 a 2  – 2.10a.5 + 25 = 100a(a – 1) + 25.

Nên 45 2  = 100.5.4 + 25 = 2025.

Tương tự:  15 2  = 225;  75 2  = 5625;  95 2  = 9025.

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

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

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

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

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

\(a.75^2-50.75+25^2\\ =75^2-2.25.75+25^2\\ =\left(75-25\right)^2=50^2=2500\)

\(b.103.97\\ =\left(100+3\right)\left(100-3\right)\\ =100^2-3^2\\ =9991\)

\(a,75^2-50.75+25^2\\ =75^2-2.75.25+25^2\\ =\left(75+25\right)^2=100^2=10000\\ b,103.97\\ =\left(100+3\right).\left(100-3\right)\\ =100^2-3^2=10000-9=9991\)

\(\left(780^2-220^2\right):\left(125^2+150\cdot125+75^2\right)\)

\(=\dfrac{1000\cdot540}{200^2}\)

\(=\dfrac{10000\cdot54}{40000}=\dfrac{54}{4}=\dfrac{27}{2}\)