Bài 1:

a,$127^2+146.127+73^2=127^2+2.127.73+73^2$$=\left(127+73\right)^2=200^2=40000$

b,$9^8.2^8-\left(18^4-1\right)\left(18^4+1\right)$

$18^8-\left(18^8-1\right)=1$

$c,100^2-99^2+98^2-97^2+...+2^2-1$

$=\left(100-99\right)\left(100+99\right)+\left(98-97\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)$$=199+195+...+3$

áp dụng công thức Gauss ta đc đáp án là:10100

d, mk khỏi ghi đề dài dòng:

$\dfrac{\left(780-220\right)\left(780+220\right)}{\left(125+75\right)^2}=\dfrac{560000}{40000}=14$Bài 2:

$A=\left(2-1\right)\left(2+1\right)$$\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)$

$A=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)$Cứ tiếp tục ta đc $A=2^{32}-1< B=2^{32}$

$\left(3-1\right)C=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)...\left(3^2+16\right)$giải như câu a đc:$\left(3-1\right)C=3^{32}-1$

$\Rightarrow C=\dfrac{3^{32}-1}{3-1}=\dfrac{3^{32}-1}{2}< D=3^{32}-1$