(i) 4a2 = 2 × 2 × a × a
4ab = 2 × 2 × a × b
4ca = 2 × 2 × c × a
∴ −4a2 + 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) x2yz = x × x × y × z xy2z
= x × y × y × z xyz2 = x × y × z × z
∴ x2yz + xy2z + xyz2
= (x × x × y × z) + (x × y × y × z) + (x × y × z × z)
= x × y × z [x + y + z]
= xyz (x + y + z)
(iii) ax2y = a × x × x × y bxy2
= b × x × y × y cxyz = c × x × y × z
The common factors are x and y.
ax2y + bxy2 + 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)
