Question

Factorize (a²-3a)² – 5(a²-3a) - 50​

Answer 1

Given,

(a²-3a)² – 5(a²-3a) - 50​=0

To find,

Factorize (a²-3a)² – 5(a²-3a) - 50​=0.

Solution,

Let a²-3a = t, we would get

⇒  t²-5t-50=0

On factorizing we get,

⇒  t²-10t+5t-50=0

⇒  t(t-10) + 5(t-10) = 0

⇒  t-10=0 and  t+5 = 0

⇒  t = 10 and t = -5

Now, putting t as a²-3a in the next step,

⇒  a²-3a=10 and a²-3a=-5

⇒  a²-5a+2a-10=0

Taking a as common we get,

⇒  a(a-5)+2(a-5)=0

⇒  a+2=0 and a-5=0

⇒  a=-2 and a = 5

Hence, the value of a are -2 and 5.