\(263^2+74.263+37^2=263^2+2.37.263+37^2=\left(263+37\right)^2=300^2=90000\)

Áp dụng hằng đẳng thức thức 1: (a+b)²=a²+2ab+b²

Cảm ơn bạn rất nhiều!

\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^{16}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^{16}+1\right)\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)

\(=2^{32}-1\)

\(263^2+74\cdot263+37^2\)

\(=263^2+2\cdot37\cdot263+37^2\)

\(=\left(363+37\right)^2\)

\(=400^2\)

Đề:a.Cm đẳng thức:

(2+1).(2²+1).(2⁴+1).(2⁸+1).(2¹⁶+1)=2³²-1

(2+1).(2²+1).(2⁴+1).(2⁸+1).(2¹⁶+1)

=(2-1).(2+1).(2²+1).(2⁴+1).(2⁸+1).(2¹⁶+1)

=(2²-1).(2²+1).(2⁴+1).(2⁸+1).(2¹⁶+1)

=(2⁴-1).(2⁴+1).(2⁸+1).(2¹⁶+1)

=(2⁸-1).(2⁸+1).(2¹⁶⁺1)

=(2¹⁶-1).(2¹⁶+1)

=2³²-1

a: \(A=\dfrac{\left(258-242\right)\left(258+242\right)}{\left(254-246\right)\left(254+246\right)}=\dfrac{16}{8}=2\)

b: \(=\left(263+37\right)^2=300^2=90000\)

c: \(=\left(136-46\right)^2=90^2=8100\)

d: \(=50^2-49^2+48^2-47^2+...+2^2-1^2\)

=50+49+...+2+1

=51x50:2=1275

b) \(263^2+74.263+37^2\)

\(=\left(263+37\right)^2\)

\(=300^2\)

\(=90000\)

c) \(136^2-92.136+46^2\)

\(=\left(136-46\right)^2\)

\(=90^2\)

\(=8100\)

cảm ơn lê tài bảo châu nhé

\(\frac{63^2-47^2}{215^2-105^2}=\)  \(\frac{\left(63-47\right)\left(63+47\right)}{\left(215-105\right)\left(215+105\right)}\)

                           \(=\frac{16.110}{110.320}=\frac{16}{320}\)\(=\frac{1}{20}\)

các câu kia làm tương tự nha

Thanks bạn nhiều nhiều nha!

nhưng câu d với câu e mk khô hiểu lắm!

\(B=263^2+74.263+37^2\)

\(=\left(263+37\right)^2\)

\(=300^2\)

\(=90000\)

\(B=263^2+74\cdot263+37^2\)

\(=263^2+2\cdot263\cdot37+37^2\)

\(=\left(263+37\right)^2\)

\(=300^2\)

\(=90000\)

B = 263² + 74 . 263 + 37²

    = 263³  + 2 . 263 . 37 + 37²

    = ( 263 + 37 )²

    = 300² 

    = 90000

Hok tốt nha bn!!!!