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 )
