a, = x2 - 6x + 9 - 1 = (x - 3)2 - 12 = (x - 4)(x - 2)
b, = 4x2 - 4x - 3x + 3 = 4x(x - 1) - 3(x - 1) = (x - 1)(4x - 3)
c, = (x + 2)(5x - 4)
d, = 5x2 - 5x + 2x - 2 = 5x(x - 1) + 2(x - 1) = (x - 1)(5x + 2)
a) \(x^2-6x+8\)
\(=x^2-4x-2x+8\)
\(=x\left(x-4\right)-2\left(x-4\right)\)
\(=\left(x-4\right)\left(x-2\right)\)
b) \(4x^2-7x+3\)
\(=4x^2-4x-3x+3\)
\(=4x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(4x-3\right)\)
c) \(\left(3x-1\right)^2-\left(2x-3\right)^2\)
\(=9x^2-6x+1-\left(4x^2-12x+9\right)\)
\(=9x^2-6x+1-4x^2+12x-9\)
\(=5x^2+6x-8\)
\(=5x^2+10x-4x-8\)
\(=5x\left(x+2\right)-4\left(x+2\right)\)
\(=\left(x+2\right)\left(5x-4\right)\)
d) \(5x^2-3x-2\)
\(=5x^2-5x+2x-2\)
\(=5x\left(x-1\right)+2\left(x-1\right)\)
\(=\left(x-1\right)\left(5x+2\right)\)
