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Find the common factors

(i) −4a2 + 4ab − 4 ca

(ii) x2yz + xy2z + xyz2

(iii) ax2y + bxy2 + cxyz

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(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 xy2

= x × y × y × z xyz2 = x × y × z × z

∴ x2yz + xy2z + xyz

= (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 bxy

= 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)

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