a) \(\left(a^2+b^2-5\right)^2-2\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5\right)^2-\left(\sqrt{2}.ab+\sqrt{2}.2\right)^2\)
\(=\left(a^2+b^2-5-\sqrt{2}.ab-\sqrt{2}.2\right).\left(a^2+b^2-5+\sqrt{2}.ab+\sqrt{2}.2\right)\)
b) \(\left(4a^2-3a-18\right)^2-\left(4a^2+3a\right)^2\)
\(\left(4a^2-3a-18-4a^2-3a\right).\left(4a^2-3a-18+4a^2+3a\right)\)
\(=\left(-6a-18\right).\left(8a^2-18\right)\)
\(=\left(-6\right).\left(a+3\right).2.\left(4a^2-9\right)\)
\(=\left(-12\right).\left(a+3\right).\left(2a-3\right).\left(2a+3\right)\)
a) Xem lại đề
b) ( 4a2 - 3a - 18 )2 - ( 4a2 + 3a )2
= [ ( 4a2 - 3a - 18 ) - ( 4a2 + 3a ) ][ ( 4a2 - 3a - 18 ) + ( 4a2 + 3a ) ]
= ( 4a2 - 3a - 18 - 4a2 - 3a )( 4a2 - 3a - 18 + 4a2 + 3a )
= ( -6a - 18 )( 8a2 - 18 )
= -6( a + 3 ).2( 4a2 - 9 )
= -12( a + 3 )( 4a2 - 9 )
= -12( a + 3 )( 2a - 3 )( 2a + 3 )
a. ( a2 + b2 - 5 )2 - 2 ( ab + 2 )2
= ( a2 + b2 - 5 )2 - [\(\sqrt{2}\)( ab + 2 ) ]2
= [ a2 + b2 - 5 -\(\sqrt{2}\)( ab + 2 ) ] [ a2 + b2 - 5 +\(\sqrt{2}\)( ab + 2 ) ]
= ( a2 + b2 - 5 -\(\sqrt{2}\)ab - 2\(\sqrt{2}\)) ( a2 + b2 - 5 +\(\sqrt{2}\)ab + 2\(\sqrt{2}\) )
b. ( 4a2 - 3a - 18 )2 - ( 4a2 + 3a )2
= ( 4a2 - 3a - 18 - 4a2 - 3a ) ( 4a2 - 3a - 18 + 4a2 + 3a )
= ( - 6a - 18 ) ( 8a2 - 18 )
= - 6 ( a + 3 ) . 2 [ ( 2a )2 - 32 ]
= - 12 ( 2a - 3 ) ( 2a + 3 )
Câu b = - 12 ( a + 3 ) ( 2a - 3 ) ( 2a + 3 )
