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\(10x\left(x-y\right)-6y\left(y-x\right)\)
\(=10x\left(x-y\right)+6x\left(x-y\right)\)
\(=\left(10x+6x\right)\left(x-y\right)\)
\(c,3x^2+5y-3xy-5x\)
\(=\left(3x^2-3xy\right)+\left(5y-5x\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(3x-5\right)\left(x-y\right)\)
\(e,27+27x+9x^2=3\left(9+9x+x^2\right)\)
a, -x - y2 + x2 - y = (x2 - y2) - (x + y)
= (x - y)(x + y) - (x + y)
= (x + y)(x - y - 1)
b, x( x + y ) - 5x - 5y = x(x + y) - 5(x + y)
= (x - 5)(x + y)
c, x2 - 5x + 5y - y2 = (x - y)(x + y) - 5(x - y)
= (x - y)(x + y - 5)
d, 5x3 - 5x2y - 10x2 + 10xy = 5x2(x - y) - 10x(x - y)
= 5x(x - y)(x - 2)
e, 27x3 - 8y3 = (3x - 2y)(9x2 + 6xy + 4y2)
f, x2 - y2 - x - y = (x - y)(x + y) - (x + y)
= (x + y)(x - y - 1)
g, x2 - y2 - 2xy + y2 = (x2 - 2xy + y2) - y2
= (x - y)2 - y2
= (x - y - y)(x - y + y) = x(x - 2y)
h, x2 - y2 + 4 - 4x = (x2 - 4x + 4) - y2
= (x - 2)2 - y2
= (x - y - 2)(x + y - 2)
i, x3 + 3x2 + 3x + 1 - 27z3 = (x + 1)3 - 27z3
= (x+1-3z)(x2+2x+1+3xz+3z+9z2)
k, 4x2 + 4x - 9y2 + 1 = (2x + 1)2 - 9y2
= (2x - 3y + 1)(2x + 3y + 1)
m, x2 - 3x + xy - 3y = x(x - 3) + y(x - 3)
= (x - 3)(x + y)