Question

phân tích thành nhân tử

4x(y-1)-(y-1)

2xy-x²-y²+16

(x+y+z)³-x³-y³-z³

Answer 1

+ \(4x\left(y-1\right)-\left(y-1\right)\) \(=\left(y-1\right)\left(4x-1\right)\)

+ \(2xy-x^2-y^2+16\) \(=-\left(x^2-2xy+y^2-16\right)\) \(=-\left[\left(x-y\right)^2-4^2\right]\)\(=-\left(x-y-4\right)\left(x-y+4\right)\)

+ \(\left(x+y+z\right)^3-x^3-y^3-z^3\) \(=\left[\left(x+y\right)+z\right]^3-x^3-y^3-z^3\)\(=\left(x+y\right)^3+z^3+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3\)\(=x^3+y^3+z^3+3xy\left(x+y\right)+3z\left(x+y\right)\left(x+y+z\right)-x^3-y^3-z^3\)\(=3xy\left(x+y\right)+3z\left(x+y\right)\left(x+y+z\right)\) \(=3\left(x+y\right)\left(xy+xz+zy+z^2\right)\)\(=3\left(x+y\right)\left[x\left(y+z\right)+z\left(y+z\right)\right]\)\(=3\left(x+y\right)\left(y+z\right)\left(z+x\right)\)

Answer 2

+)4x(y-1)-(y-1)

=(y-1)(4x-1)

+)2xy-x²-y²+16

=-(x²-2xy+y²)+16

=-(x-y)²+16

=-(x-y-4)(x-y+4)

Answer 3

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