VT := [(5a - 3b) + 8c][(5a - 3b) - 8c] 
= (5a - 3b)^2 - 64c^2 (theo hiệu hai bình phương) 
= 25a^2 - 30ab + 9b^2 - 64c^2 (theo bình phương của hiệu) 
= 25a^2 - 30ab + 9b^2 - 16(a^2 - b^2) (vì 4c^2 = a^2 - b^2) 
= 9a^2 - 30ab + 25b^2 
= (3a - 5b)^2 (theo bình phương của hiệu).

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

\(=25a^2-30ab+9b^2-16c^2\)

\(=25a^2-30ab+9b^2-16\left(a^2-b^2\right)\)

\(=25a^2-30ab+9b^2-16c^2+16b^2\)

\(=9a^2-30ab+25b^2\)

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

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

\(\Leftrightarrow\left(5a-3b\right)^2-64c^2-\left(3a-5b\right)^2=0\)

\(\Leftrightarrow\left(5a-3b-3a+5b\right)\left(5a-3b+3a-5b\right)=64c^2\)

\(\Leftrightarrow\left(2a+2b\right)\left(8a-8b\right)=16\left(a^2-b^2\right)\)

\(\Leftrightarrow16\left(a^2-b^2\right)=16\left(a^2-b^2\right)\left(true\right)\)

Vậy \(\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(3a-5b\right)^2\)khi \(a^2-b^2=4c^2\)

$\mathrm{(5}a-3b+8c)(5a-3b-8c)$

$={}^{}-{}^{}$

$={}^{}-16.4{}^{}$

Thay ${}^{}-{}^{}=4{}^{}$ ta có :

$=25{}^{}-30ab+9{}^{}-16({}^{}-{}^{})$

$=25{}^{}-30ab+9{}^{}-16{}^{}+16{}^{}$

$=9{}^{}-30ab+25{}^{}$

$={}^{}\left(\mathrm{đp}cm\right)$

Ta có : \(\left(5a-3b+8c\right)\left(5a-3b-8c\right)\)

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

\(=\left(5a-3b\right)^2-64c^2\)

\(=\left(5a-3b\right)^2-16.4c^2\)

\(=\left(5a-3b\right)^2-16\left(a^2-b^2\right)\)

\(=25a^2-30ab+9b^2-16a^2+16b^2\)

\(=9a^2-30ab+25b^2\)

\(=\left(3a-5b\right)^2\left(đpcm\right)\)

Ta có:

\(VT=(5a-3b+8c).(5a-3b-8c)\)

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

Mà \(a^2-b^2=4c^2\) nên:

\(VT=25^2-30ab+9b^2-16.\left(a^2-b^2\right)\)

\(=9a^2-30ab+25b^2\)

\(=\left(3a-5b\right)^2=VP\)

\(\Rightarrow\) Đpcm.

VT= (5a-3b)^2 - 64c^2=25a^2-30ab + 9b^2 -16a^2+16b^2=9a^2-30ab+25b^2= (3a-5b)^2 = VP (đpcm)

Xét VT ta có :

VT = ( 5a - 3b + 8c )( 5a - 3b - 8c )

      = ( 5a - 3b )² - ( 8c )²

      = 25a² - 30ab + 9b² - 64c²

      = 25a² - 30ab + 9b² - 16.4c²

      = 25a² - 30ab + 9b² - 16( a² - b² )

      = 25a² - 30ab + 9b² - 16a² + 16b²

      = 9a² - 30ab + 25b²

      = ( 3a - 5b )² = VP

=> đpcm

biến đổi vế trái 

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

\(\Leftrightarrow25a^2-30ab+9b^2-64c^2\)

\(\Leftrightarrow25a^2-30ab+9b^2-16\left(a^2-b^2\right)\)

\(\Leftrightarrow\left(25a^2-16a^2\right)-30ab+\left(9b^2+16b^2\right)\)

\(\Leftrightarrow9a^2-30ab+25b^2\)

\(\Leftrightarrow\left(3a-5b\right)^2\)  (điều cần c/m)