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\(263^2+74.263+37^2=263^2+2.37.263+37^2=\left(263+37\right)^2=300^2=90000\)
Áp dụng hằng đẳng thức thức 1: (a+b)2=a2+2ab+b2
\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=2^{32}-1\)
\(263^2+74\cdot263+37^2\)
\(=263^2+2\cdot37\cdot263+37^2\)
\(=\left(363+37\right)^2\)
\(=400^2\)
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) \(136^2-92.136+46^2\)
\(=\left(136-46\right)^2\)
\(=90^2\)
\(=8100\)
\(\frac{63^2-47^2}{215^2-105^2}=\) \(\frac{\left(63-47\right)\left(63+47\right)}{\left(215-105\right)\left(215+105\right)}\)
\(=\frac{16.110}{110.320}=\frac{16}{320}\)\(=\frac{1}{20}\)
các câu kia làm tương tự nha
\(B=263^2+74.263+37^2\)
\(=\left(263+37\right)^2\)
\(=300^2\)
\(=90000\)
\(B=263^2+74\cdot263+37^2\)
\(=263^2+2\cdot263\cdot37+37^2\)
\(=\left(263+37\right)^2\)
\(=300^2\)
\(=90000\)
\(263^2+74.263+37^2\)
\(=69169+74.263+1369\)
\(=69169+19462+1369\)
\(=88631+1369\)
\(=90000\)