Question

Find the common factors

(i) −16z + 20z³

(ii) 20l²m + 30 alm

(iii) 5x²y − 15xy²

(iv) 10a² − 15b² + 20c²

Answer 1

(i) 16z = 2 × 2 × 2 × 2 × z 20z³ 

= 2 × 2 × 5 × z × z × z

∴ −16z + 20z³ 

= − (2 × 2 × 2 × 2 × z) + (2 × 2 × 5 × z × z × z)

= (2 × 2 × z) [− (2 × 2) + (5 × z × z)]

= 4z (− 4 + 5z²)

(ii) 20l²m = 2 × 2 × 5 × l × l × m 30alm 

= 2 × 3 × 5 × a × l × m

∴ 20l²m + 30alm 

= (2 × 2 × 5 × l × l × m) + (2 × 3 × 5 × a × l × m) 

= (2 × 5 × l × m) [(2 × l) + (3 × a)]

= 10lm (2l + 3a)

(iii) 5x²y = 5 × x × x × y

15xy² = 3 × 5 × x × y × y

The common factors are 5, x, and y.

∴ 5x²y − 15xy² 

= (5 × x × x × y) − (3 × 5 × x × y × y) 

= 5 × x × y [x − (3 × y)]

= 5xy (x − 3y)

(iv) 10a² = 2 × 5 × a × a 15b² = 3 × 5 × b × b

20c² = 2 × 2 × 5 × c × c

The common factor is 5.

10a² − 15b² + 20c² = (2 × 5 × a × a) − (3 × 5 × b × b) + (2 × 2 × 5 × c × c)

= 5 [(2 × a × a) − (3 × b × b) + (2 × 2 × c × c)]

= 5 (2a² − 3b² + 4c²)