a) \(x^2-y^2-x+y\)
\(=\left(x^2-y^2\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-1\right)\)
b) \(a^3x-ab+b-x\)
\(=\left(a^3x-x\right)-\left(ab-b\right)\)
\(=\left(a^3-1\right)x-\left(a-1\right)b\)
\(=\left(a-1\right)\left(a^2+a+1\right)x-\left(a-1\right)b\)
\(=\left(a-1\right)\left[\left(a^2+a+1\right)x-b\right]\)
a) x² - y² - x + y
= (x² - y²) - (x - y)
= (x - y)(x + y) - (x - y)
= (x - y)(x + y + 1)
b) a³x - ab + b - x
= (a³x - x) - (ab - b)
= x(a³ - 1) - b(a - 1)
= x(a - 1)(a² + a + 1) - b(a - 1)
= (a - 1)[x(a² + a + 1) - b]
