a) 5x - 15y = 5(x - 3y)

b) \(\dfrac{3}{5}\)x2 + 5x4 - x2 - y

= \(\dfrac{3}{5}\)x2 + 5x2.x2 - x2 - y

= x2(\(\dfrac{3}{5}\) + 5x2 -1) - y

c) 14x2y2 - 21xy2 + 28x2y

= 7xy.xy - 7xy.3y + 7xy.4x

= 7xy(xy - 3y + 4x)

= 7xy[(xy - 3y) + 4x]

= 7xy[y(x - 3) +4x]

d) \(\dfrac{2}{7}x\)(3y - 1) - \(\dfrac{2}{7}y\)(3y - 1)

= (3y - 1).(\(\dfrac{2}{7}x\) - \(\dfrac{2}{7}y\) )

= (3y - 1).[\(\dfrac{2}{7}\)(x - y)]

e) x3 - 3x2 + 3x - 1

= x2.x - 3x.x + 3.x - 1

= x(x2-3x+3) - 1

g) 27x3 + \(\dfrac{1}{8}\)

= (3x)3 + \(\left(\dfrac{1}{2}\right)^3\)

= (3x + \(\dfrac{1}{2}\)).(9x2 - \(\dfrac{3}{2}\)x + \(\dfrac{1}{4}\))

h) (x+y)3 - (x-y)3

= 2(3x2y) + 2y3

f) (x+y)2 - 4x2

= -3x2 + y(2x + y)