a)
\(5x\left(x-1\right)-x+1\)
= \(5x\left(x-1\right)-\left(x-1\right)\)
= \(\left(x-1\right)\left(5x-1\right)\)
b)
\(2.\left(x+5\right)-x^2-5x\)
= \(2.\left(x+5\right)-x\left(x+5\right)\)
= \(\left(x+5\right)\left(2-x\right)\)
c)
\(x^2-2xy-4x^2+y^2\)
= \(-2x^2-x^2-2xy+y^2\)
= \(\left(-2x^2-2xy\right)-\left(x^2-y^2\right)\)
= \(-2x\left(x+y\right)-\left(x-y\right)\left(x+y\right)\)
= \(\left(x+y\right)\left(-2x-x+y\right)\)
= \(\left(x+y\right)\left(-3x+y\right)\)
d) Cách 1:
\(x^2-2x-3\)
= \(\left(x^2-2x+1\right)-4\)
= \(\left(x-1\right)^2-2^2\)
= \(\left(x-1-2\right)\left(x-1+2\right)\)
= \(\left(x-3\right)\left(x+1\right)\)
Cách 2:
\(x^2-2x-3\)
= \(\left(x^2-x\right)-\left(x-1\right)-4\)
= \(x\left(x-1\right)-\left(x-1\right)-2^2\)
= \(\left(x-1\right)\left(x-1\right)-2^2\)
= \(\left(x-1\right)^2-2^2\)
= \(\left(x-1-2\right)\left(x-1+2\right)\)
= \(\left(x-3\right)\left(x+1\right)\)
e) \(2x^2+5x^2.3\) = \(x^2\left(2+15\right)\) = \(17.x^2\)