Question

a6 - 18a3 + 125 -- Factorise

Answer 1

Given: The expression a^6 - 18a^3 + 125

To find: Factorise the given expression.

Solution:

• Now we have given a^6 - 18a^3 + 125

• We can write 18a^3 as 45a^3 - 27a^3 

• So the expression becomes:

              a^6 - 27a^3 + 125 + 45a^3 

• Now solving this, we get:

             (a²)^3 + (-3a)^3 + (5)^3 - 3(a²)(-3a)(5) 

• Now, we know that:

             a^3 + b^3 + c^3 - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca) 

• So, applying this, we get:

             (a² - 3a + 5){(a^4) + 9a² + 25 + 3(a^3) + 15a - 5a²} 

             (a² - 3a + 5){(a^4) + 3a^3 + 4a² + 15a + 25}

Answer:

        So after factorisation, answer comes out to be:

      (a² - 3a + 5){(a^4) + 3a^3 + 4a² + 15a + 25}