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b) \(x^3-4x^2-12x+27=\left(x^3+27\right)-\left(4x^2+12x\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
d) \(x^{16}-1=\left(x^4-1\right)\left(x^4+1\right)=\left(x^2-1\right)\left(x^2+1\right)\left(x^4+1\right)\)
\(x^8+x+1\)
\(=x^8+x^7+x^6-x^7-x^6-x^5+x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left(x^6-x^5+x^3-x^2+1\right)\)
a) x2 - 6x + 9 - 16 = x2 - 6x - 7 = x2 + x - 7x - 7 = x(x+1) - 7(x+1) = (x-7)(x+1)
b) x4 - 64 = (x2 - 8)(x2 + 8)
(x2 - 2.x.3 +32 ) - 42
(x-3)2 - 42
(x-3-4)(x-3+4)
b)
(x2)2 - 82
(x2-8)(x2+8)
\(\left(x+3\right)^2-16\)
\(=\left(x+3-4\right)\left(x+3+4\right)\)
\(=\left(x-1\right)\left(x+7\right)\)
\(=x^2.\left(x-1\right)-16.\left(x-1\right)\)
\(=\left(x-1\right).\left(x^2-16\right)\)
\(=\left(x-1\right).\left(x-4\right).\left(x+4\right)\)
x2.( x - 1 ) + 16.( 1 - x )
= x2.( x - 1 ) - 16.( x - 1 )
= ( x - 1 ).( x2 - 16 )
= ( x - 1 ).( x2 - 42 )
= ( x - 1 ).( x + 4 ).( x - 4 )
Lời giải
\(=x^2\left(x-1\right)-16\left(x-1\right)\)
\(=\)\(\left(x-1\right)\left(x^2-16\right)\)
\(=\left(x-1\right)\left(x^2-4^2\right)\)
\(=\left(x-1\right)\left(x+4\right)\left(x-4\right)\)
\(9\left(x-1\right)^2-16\left(x-2\right)^2\)
\(=\left(3x-3\right)^2-\left(4x-8\right)^2\)
\(=\left(3x-3-4x+8\right)\left(3x-3+4x-8\right)\)
\(=\left(-x+5\right)\left(7x-11\right)\)
Mình nhờ bạn giải giúp mình bài này đc không?