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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: \(\left(a^4-3a^2+9\right)\left(a^2+3\right)-\left(a^2+3\right)^3\)
\(=a^6+27-a^6-9a^4-27a^2-27\)
\(=-9a^4-27a^2\)
a: \(B=\dfrac{x-4\sqrt{x}+4\sqrt{x}+16}{x-4}\cdot\dfrac{\sqrt{x}+2}{x+16}=\dfrac{1}{\sqrt{x}-2}\)
b: Khi x=9 thì B=1/(3-2)=1
b: \(8x^2-48x+6xy-36y\)
\(=8x\left(x-6\right)+6y\left(x-6\right)\)
\(=2\left(x-6\right)\left(4x+3y\right)\)
d: \(a^2-2ab+b^2-4\)
\(=\left(a-b\right)^2-4\)
\(=\left(a-b-2\right)\left(a-b+2\right)\)
\(A=8\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-81^{16}\)
\(A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-81\)
\(A=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)-81^{16}\)
\(A=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)-81^{16}\)
\(A=\left(3^{16}-1\right)\left(3^{16}+1\right)-81^{16}\)
\(A=3^{32}-1-81^{16}\)
A = 8.( 32 + 1 ).( 34 + 1 ).( 38 + 1).( 316 + 1 ) - 8116
A = ( 32 - 1).( 32 + 1 ).( 34 + 1 ).( 38 + 1).( 316 + 1 ) - 8116
A = ( 34 - 1 ).( 34 + 1 ).( 38 + 1).( 316 + 1 ) - 8116
A = ( 38 - 1 ).( 38 + 1).( 316 + 1 ) - 8116
A = ( 316 - 1 ).( 316 + 1 ) - 8116
A = ( 332 - 1 ) - 8116
A = -364
A = (a^2+4).(a^2-4)/(a^4+4a^2)-(4a^3+16a)+(4a^2+16)
= (a^2+4).(a^2-4)/(a^2+4).(a^2-4a+4)
= (a^2+4).(a-2).(a+2)/(a^2+4).(a-2)^2
= a+2/a-2
Tk mk nha