a) \(A=\dfrac{356^2-144^2}{256^2-244^2}=\dfrac{\left(356+144\right)\left(356-144\right)}{\left(256+244\right)\left(256-244\right)}=\dfrac{500\cdot212}{500\cdot12}=\dfrac{212}{12}=\dfrac{53}{3}\)
b) \(B=253^2+94\cdot253+47^2=253^2+2\cdot47\cdot253+47^2=\left(253+47\right)^2=300^2=90000\)
c) \(C=163^2-92\cdot136+46^2=163^2-92\cdot163+46^2+92\cdot27\)
\(C=\left(163^2-2\cdot46\cdot163+46^2\right)+92\cdot27\)
\(C=\left(163-46\right)^2+92\cdot27\)
\(C=117^2+92\cdot27\)
\(C=13689+2484=16173\)
d) \(D=\left(100^2+98^2+...+2^2\right)-\left(99^2+97^2+...+1^2\right)\)
\(D=100^2-99^2+98^2-...+2^2-1^2\)
\(D=\left(100^2-99^2\right)+\left(98^2-97^2\right)+...+\left(2^2-1^2\right)\)
\(D=\left(100-99\right)\left(100+99\right)+\left(98-97\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)\)
\(D=100+99+98+97+...+2+1\)
Dãy số D có (100-1)+1 = 100 (chữ số)
Mỗi chữ số trong dãy cách nhau 1 đơn vị nên
\(D=\left(100+1\right)\cdot\left(100:2\right)=101\cdot50=5050\)
