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a) \(a^4-4a^3+8a^2-16a+16\)
\(=a^4-4a^3+4a^2+4a^2-16a+16\)
\(=\left(a^4-4a^3+4a^2\right)+\left(4a^2-16a+16\right)\)
\(=a^2\left(a^2-4a+4\right)+4\left(a^2-4a+4\right)\)
\(=a^2\left(a^2-2.a.2+2^2\right)+4\left(a^2-2.a.2+2^2\right)\)
\(=a^2\left(a-2\right)^2+4\left(a-2\right)^2\)
\(=\left(a-2\right)^2\left(a^2+4\right)\)
\(3y^2\left(a-3x\right)-a\left(a-3x\right)=\left(3y^2-a\right)\left(a-3x\right)\)
\(A=4\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(2A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(2A=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(2A=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(2A=\left(3^{16}-1\right)\left(3^{16}+1\right)\)
\(2A=3^{32}-1\Rightarrow A=\frac{3^{32}-1}{2}\)
a/ (x+y)3-(x-y)3-2y3
= (x3+3x2y+3xy2+y3)-(x3-3x2y+3xy2-y3)-2y3
= x3+3x2y+3xy2+y3-x3+3x2y-3xy2+y3-2y3
= 6xy2
b/ (x+2)(x2-2x+4)-(16-x3)
= x3-2x2+4x+2x2-4x+8-16+x3
= 2x3-8
c/ (2a+b)(4a2-2ab+b2)-(2a-b)(4a2+2ab+b2)
= (8a3+b3)-(8a3-b3)
= 8a3+b3-8a3+b3
= 2b3
ta có : \(\frac{a^3-4a^2-a+4}{a^3-7a^2+14a-8}\)
= \(\frac{\left(a-1\right)\left(a+1\right)\left(a-4\right)}{\left(a-4\right)\left(a-2\right)\left(a-1\right)}\)
= \(\frac{a+1}{a-2}\)
nhớ nha
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