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a) x4 + x2 - 27x - 9
= (x4 - 27x) + x2 - 9
= x(x3 - 27) + (x - 3)(x + 3)
= x(x - 3)(x2 + 3x + 9) + (x - 3)(x + 3)
= (x - 3)(x3 + 3x2 + 9x + x + 3)
= (x - 3)(x3 + 3x2 + 10x + 3)
b) x2 - xy - x + y
= x(x - y) - (x - y)
= (x - 1)(x - y)
c) xy + 4 - x2 + 2y
= (xy + 2y) - (x2 - 4)
= y(x + 2) - (x - 2)(x + 2)
= (x + 2)(y - x + 2)
d) xy + y - 2(x + 1)
= y(x + 1) - 2(x + 1)
= (y - 2)(x + 1)
a) \(xy+y-2x-2\)
\(=y\left(x+1\right)-2\left(x+1\right)\)
\(=\left(x+1\right)\left(y-2\right)\)
b) \(xy+1+x+y\)
\(=y\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(y+1\right)\)
c) \(x\left(x-1\right)+y\left(x-1\right)+z\left(x-1\right)\)
\(=\left(x-1\right)\left(x+y+z\right)\)
a) =y^2-(x+3)^2
=(y-x-3)(y+x+3).
b)
=x^2-(y^2+2y+1)
=x^2-(y+1)^2
=(x-y-1)(x+y+1)
c)
=(5x^2-15x)(xy-2y)
=5x(x-3)y(x-2)
=5xy(x-2)(x-3).
a) Theo mình thì đề sai ấy! Có z kia.
b) \(\left(x+y\right)^2-\left(x^2-y^2\right)=\left(x+y\right)^2-\left(x+y\right)\left(x-y\right)=\left(x+y\right)\left(x+y-x+y\right)=\left(x+y\right)\left(2y\right)\)
a) \(xy+y-2x-2\)
\(=y\left(x+1\right)-2\left(x+1\right)\)
\(=\left(x+1\right)\left(y-2\right)\)
b) \(xy+1+x+y\)
\(=y\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(y+1\right)\)
c) \(x^2+xy-x-y+xz-z\)
\(=\left(x^2-x\right)+\left(xy-y\right)+\left(xz-z\right)\)
\(=x\left(x-1\right)+y\left(x-1\right)+z\left(x-1\right)\)
\(=\left(x-1\right)\left(x+y+z\right)\)
\(x^2+y^2-x^2y^2+xy-x-y.\)
\(=\left(x^2-x^2y^2\right)+\left(y^2-y\right)+\left(xy-x\right)\)
\(=x^2\left(1-y^2\right)+y\left(y-1\right)+x\left(y-1\right)\)
\(=x^2\left(1-y\right)\left(1+y\right)-y\left(1-y\right)-x\left(1-y\right)\)
\(=\left(1-y\right)\left(x^2\left(1+y\right)-y-x\right)\)
\(=\left(1-y\right)\left(x^2+x^2y-y-x\right)\)
\(=\left(1-y\right)\left[\left(x^2-x\right)+\left(x^2y-y\right)\right]\)
\(=\left(1-y\right)\left[x\left(x-1\right)+y\left(x^2-1\right)\right]\)
\(=\left(1-y\right)\left[x\left(x-1\right)+y\left(x-1\right)\left(x+1\right)\right]\)
\(=\left(1-y\right)\left[\left(x-1\right)\left(x+y\left(x-1\right)\right)\right]\)
\(=\left(1-y\right)\left(x-1\right)\left(x+yx+y\right)\)
b: \(\left(xy-8\right)^2-1\)
\(=\left(xy-8\right)^2-1^2\)
\(=\left(xy-8-1\right)\left(xy-8+1\right)\)
=(xy-7)(xy-9)
a: \(xy+y^2-x-y\)
\(=y\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(y-1\right)\)
`#3107.10117`