Question

Factorise: 27x^3-108x^2+144x-64

Answer 1

p(x)=27x^3-108x^2+144x-63
g(x)=1
p(1)=27*1^3-108*1^2+144*1-63 =0
therefore x=1 is a factor of px
or x-1 is a factor of px
after this look above in the picture
I have solved the sum using factor theorem

Answer 2

Answer:

${(3x - 4)}^{3}$

Step-by-step explanation:

Since,

${(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)$

Therefore,

$27 {x}^{3} - 64 + 144x - 108 {x}^{2}$

$= {(3x)}^{3} - {(4)}^{3} - 3(3x)(4)(3x - 4)$

$= {(3x - 4)}^{3}$