Question

Phân tích thành nhân tử:

a) \(x^4-x^2-2x-1\)

b) \(x^2+25+10x-y^2-2y-1\)

c) \(x^2+4y^2-4xy-z^2+6z-9\)

d) \(x^2-3z\left(3z-2\right)-12xy-1+36y^2\)

e) \(4a^2b^2-\left(a^2+b^2-c^2\right)\)

f) \(x^3+3x^2-9x-27\)

g) \(x^{m+4}+x^{m+3}-x-1\)

Answer 1

a) \(x^4-x^2-2x-1\)

\(=\left(x^2\right)^2-\left(x+1\right)^2\)

\(=\left(x^2-x-1\right)\left(x^2+x+1\right)\)

Answer 2

b)\(x^2+25+10x-y^2-2y-1\)

\(=\left(x+5\right)^2-\left(y-1\right)^2\)

\(=\left(x+5-y+1\right)\left(x-5+y-1\right)\)

\(=\left(x-y+6\right)\left(x+y-6\right)\)

Answer 3

c)\(x^2+4y^2-4xy-z^2+6z-9\)

\(=\left(x-2y\right)^2-\left(z-3\right)^2\)

\(=\left(x-2y-z+3\right)\left(x-2y+z-3\right)\)

Answer 4

d: \(=x^2+6z-9z^2-12xy-1+36y^2\)

\(=\left(x-6y\right)^2-\left(3z-1\right)^2\)

\(=\left(x-6y-3z+1\right)\left(x-6y+3z-1\right)\)

e: \(=\left(2ab-a^2-b^2+c^2\right)\left(2ab+a^2+b^2-c^2\right)\)

\(=\left[c^2-\left(a-b\right)^2\right]\left[\left(a+b\right)^2-c^2\right]\)

\(=\left(c-a+b\right)\left(c+a-b\right)\left(a+b-c\right)\left(a+b+c\right)\)