(i) 4a^{2} = 2 × 2 × a × a

4ab = 2 × 2 × a × b

4ca = 2 × 2 × c × a

∴ −4a^{2} + 4ab − 4ca

= − (2 × 2 × a × a) + (2 × 2 × a × b) − (2 × 2 × c × a)

= 2 × 2 × a [− (a) + b − c]

= 4a (−a + b − c)

(ii) x^{2}yz = x × x × y × z xy^{2}z

= x × y × y × z xyz^{2} = x × y × z × z

∴ x^{2}yz + xy^{2}z + xyz^{2 }

= (x × x × y × z) + (x × y × y × z) + (x × y × z × z)

= x × y × z [x + y + z]

= xyz (x + y + z)

(iii) ax^{2}y = a × x × x × y bxy^{2 }

= b × x × y × y cxyz = c × x × y × z

The common factors are x and y.

ax^{2}y + bxy^{2} + cxyz

= (a × x × x × y) + (b × x × y × y) + (c × x × y × z)

= (x × y) [(a × x) + (b × y) + (c × z)]

= xy (ax + by + cz)