Lời giải:

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

\(=25a^2+9b^2-30ab-(8c)^2\)

\(=(9a^2+25b^2-30ab)+(16a^2-16b^2)-64c^2\)

\(=(3a-5b)^2+16.4c^2-64c^2\)

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

hey Xuân phẹt oy là tui đây

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).

xét hiệu\(\left(5a-3b+8c\right)\left(5a-3b-8c\right)-\left(3a-5b\right)^2=0\)

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

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

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

\(\left(2a+2b\right)\left(8a-8b\right)-64c^2=0\)

\(16a^2-16ab+16ab-16b^2-64c^2=0\)

\(16a^2-16b^2-64c^2=0\)

\(16\left(a^2-b^2\right)-64c^2=0\)

\(16\times4c^2-64c^2=0\)

\(64c^2-64c^2=0\left(dpcm\right)\)

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

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

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

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

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

( 5a - 3b + 8c )( 5a - 3b - 8c ) 

= [ ( 5a - 3b ) + 8c ][( 5a - 3b ) - 8c ]

= ( 5a - 3b )² - ( 8c )²

= 25a² - 30ab + 9c² - 64c²

= 25a² - 30ab + 9c² - 16.4c²

= 25a² - 30ab + 9c² - 16( a² - b² )

= 25a² - 30ab + 9c² - 16a² + 16b²

= 9a² - 30ab + 25b²

= ( 3a - 5b )² ( đpcm )

(5a-3b+8c)(5a-3b-8c) = (5a-3b)^2  - 64c^2 = 25a^2  + 9b^2 - 30ab - 16(a^2 - b^2) = 9a^2 - 30ab + 25b^2 = (3a-5b)^2

=> dpcm

do copy

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

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

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

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

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

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