bài 1: ta có : \(\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(3a-5b\right)^2\)

\(\Leftrightarrow\left(5a-3b\right)^2-\left(8c\right)^2=\left(3a-5b\right)^2\) \(\Leftrightarrow\left(5a-3b\right)^2-\left(3a-5b\right)^2=\left(8c\right)^2\)

\(\Leftrightarrow\left(5a-3b-3a+5b\right)\left(5a-3b+3a-5b\right)=\left(8c\right)^2\)

\(\Leftrightarrow\left(2a+2b\right)\left(8a-8b\right)=64c^2\) \(\Leftrightarrow16\left(a+b\right)\left(a-b\right)=64c^2\)

\(\Leftrightarrow a^2-b^2=4c^2\left(đpcm\right)\)

bài 2 : bài này yc CM j bn ?? ?

bài 3 : a) ta có : \(a^2+b^2+c^2=ab+bc+ca\)

\(\Leftrightarrow2a^2+2b^2+2c^2=2ab+2bc+2ca\)

\(\Leftrightarrow a^2-2ab+b^2+b^2-2bc+c^2+c^2-2ca+a^2=0\)

\(\Leftrightarrow\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2=0\)

\(\Leftrightarrow a=b=c\left(đpcm\right)\)

b) ta có : \(\left(a+b+c\right)^2=3\left(a^2+b^2+c^2\right)\)

\(\Leftrightarrow a^2+b^2+c^2+2ab+2bc+2ca=3a^2+3b^2+c^2\)

\(\Leftrightarrow ab+bc+ca=a^2+b^2+c^2\) \(\Rightarrow\) giống câu a

c) ta có : \(\left(a+b+c\right)^2=3\left(ab+bc+ca\right)\)

\(\Leftrightarrow a^2+b^2+c^2+2ab+2bc+2ca=3ab+3bc+3ca\)