a: Ta có: \(\left(a^2-1\right)^3-\left(a^4+a^2+1\right)\left(a^2-1\right)\)

\(=a^6-3a^4+3a^2-1-\left(a^6-1\right)\)

\(=-3a^4+3a^2\)

b: Ta có: \(\left(a^4-3a^2+9\right)\left(a^2+3\right)-\left(a^2+3\right)^3\)

\(=a^6+27-a^6-9a^4-27a^2-27\)

\(=-9a^4-27a^2\)

\(N=a^3+b^3+3ab\)

\(=\left(a+b\right)^3-3ab\left(a+b\right)+3ab\)

=1

\(M=\left(a^2+b^2+2-a^2-b^2+2\right)\left[\left(a^2+b^2+2\right)^2+\left(a^2+b^2+2\right)\left(a^2+b^2-2\right)+\left(a^2+b^2-2\right)^2\right]-12\left(a^2+b^2\right)^2\\ M=4\left(a^4+b^4+4+4a^2+4b^2+2a^2b^2+\left(a^2+b^2\right)^2-4+a^4+b^4+4-4a^2-4b^2+2a^2b^2\right)-12\left(a^4+2a^2b^2+b^4\right)\\ M=4\left(3a^4+3b^4+4+6a^2b^2\right)-12\left(a^4+2a^2b^2+b^4\right)\\ M=4\left(3a^4+3b^4+4+6a^2b^2-3a^4-6a^2b^2-3b^4\right)\\ M=4\cdot4=164\)

C = a 2 − a a + a + 1 − a 2 + a a − a + 1 + a + 1         ( D K : a ≥ 0 ) C = a ( a ) 3 − 1 a + a + 1 − a ( a ) 3 + 1 a − a + 1 + a + 1 = a ( a − 1 ) − a ( a + 1 ) + a + 1 = a − a − a − a + a + 1 = a - 1 2

\(a,Sửa:a^2-b^2=\left(a-b\right)\left(a+b\right)\\ b,=a^4+2a^2b^2+b^4-2a^2b^2\\ =\left(a^2+b^2\right)^2-2a^2b^2=\left(a^2+b^2-ab\sqrt{2}\right)\left(a^2+b^2+ab\sqrt{2}\right)\\ c,=a\left(a-1\right)\\ d,=a^2-a-2a+2=\left(a-1\right)\left(a-2\right)\\ e,=a^2-2a-3a+6=\left(a-2\right)\left(a-3\right)\\ g,=a^2-3a-4a+12=\left(a-3\right)\left(a-4\right)\)

a) A = ( 6 a   +   2 ) 2 .             b) B = 1 4 ( 3 x + 1 ) 2 .