Question

pls answer this fast and i will mrk it as brainliest!!!!!
factorise (x^2-5x)^2-30(x^2-5x)+144

Answer 1

Given,

(x²-5x)² - 30(x² - 5x) + 144
let (x²-5x) = y
So, equation will be :-
y² - 30y +144

→y² -24y - 6y +144

→y(y-24) - 6(y-24)

→ (y-6)(y-24)...............(i)
Now, putting values of y and factorise Again,

y-6 = x² -5x -6

= x² -6x + x -6

= x(x-6)+ 1(x-6)

=(x+1) (x-6)

and

(y-24) = x² -5x - 24

= x² -8x +3x - 24

= x(x-8) + 3(x-8)

= (x+3) (x-8)
Therefore,

(y-6)(y-24) = (x+1)(x-6)(x+3)(x-8)
or,

(x²-5x)² - 30(x² - 5x) + 144= (x+1)(x-6)(x+3)(x-8)