a) \(85^2-15^2=\left(85-15\right)\left(85+15\right)=70.100=7000\)

b) \(93^3+21.93^2+3.49.93+343\)

\(=93^3+3.7.93^2+3.7^2.93+7^3\)

\(=\left(93+7\right)^3\)

\(=100^3=1000000\)

c) \(73^2-13^2-10^2+20.13\)

\(=73^2-\left(13^2+10^2-20.13\right)\)

\(=73^2-\left(13-10\right)^2\)

\(=73^2-3^2\)

\(=\left(73+3\right)\left(73-3\right)\)

\(=76.70=5320\)

d) Viết = Latex hộ mình

a) Ta có: \(85^2-15^2\)

\(=\left(85-15\right)\left(85+15\right)\)

\(=70\cdot100=7000\)

b) Ta có: \(93^3+21\cdot93^2+3\cdot49\cdot93+343\)

\(=93^3+3\cdot93^2\cdot7+3\cdot93+7^2+7^3\)

\(=\left(93+7\right)^3\)

\(=100^3=1000000\)

c) Ta có: \(73^2-13^2-10^2+20\cdot13\)

\(=73^2-\left(13^2+10^2-20\cdot13\right)\)

\(=73^2-\left(13^2-2\cdot13\cdot10+10^2\right)\)

\(=73^2-\left(13-10\right)^2\)

\(=73^2-3^2=\left(73-3\right)\left(73+3\right)\)

\(=70\cdot76=5320\)

a) \(85^2-15^2=\left(85-15\right)\left(85+15\right)=70.100=7000\)

c) \(73^2-13^2-10^2+20.13\)

\(=73^2-\left(13^2+10^2-20.13\right)\)

\(=73^2-\left(13^2-2.13.10+10^2\right)\)

\(=73^2-\left(13-10\right)^2\)

\(=73^2-3^2\)

\(=\left(73-3\right)\left(73+3\right)\)

\(=70.76\)

\(=5320\)

d)Viết đề = công thức trực quan hộ mình

\(A=\dfrac{97^3+83^3}{180}-97.83\)

\(A=\dfrac{\left(97+83\right)\left(97^2-97.83+83^2\right)}{180}-97.83\)

\(A=\dfrac{180\left(97^2-97.83+83^2\right)}{180}-97.83\)

\(A=97^2-97.83+83^2-97.83\)

\(A=97^2-2.97.83+83^2\)

\(A=\left(97-83\right)^2\)

\(A=14^2\)

\(A=196\)

\(a,\frac{97^3+83^3}{180}-97.83\)

\(=\frac{\left(97+83\right)\left(97^2-97.83+83^2\right)}{180}-97.83\)

\(=\frac{180\left(97^2-97.83+83^2\right)}{180}-97.83\)

\(=97^2-97.83+83^2-97.83\)

\(=97^2+83^2-2.97.83\)

\(=\left(97-83\right)^2\)

\(=14^2=196\)

\(R=\frac{43^2-11^2}{\left(36,5\right)^2-\left(27,5\right)^2}\)

    \(=\frac{\left(43-11\right)\left(43+11\right)}{\left(36,5-27,5\right)\left(36,5+27,5\right)}\)

    \(=\frac{32.54}{9.64}\)

    \(=\frac{6}{2}=3\)

Bạn viết sai đề bài rồi

\(S=\frac{97^3+83^3}{180}-97.83\)

  \(=\frac{\left(97+83\right)\left(97^2-97.83+83^2\right)}{180}-97.83\)

   \(=97^2-97.83+83-97.83\)

    \(=\left(97-83\right)^2=14^2=196\)

Trả lời:

\(R=\frac{43^2-11^2}{36,5^2-27,5^2}\)

\(R=\frac{\left(43-11\right).\left(43+11\right)}{\left(36,5-27,5\right).\left(36,5+27,5\right)}\)

\(R=\frac{32.54}{9.64}\)

\(R=3\)

Đề bài sai bạn nhé 

\(S=\frac{97^3+83^3}{180}-97.83\)

\(S=\frac{\left(97+83\right).\left(97^2-97.23+83^2\right)}{180}-97.83\)

\(S=97^2-97.83+83^2-97.83\)

\(S=97^2-2.97.83+83^2\)

\(S=\left(97-83\right)^2\)

\(S=14^2\)

\(S=196\)

17x93+116x83+17x233=15170

=15170