Question

By using this identity "a³ + b³ = (a + b) (a² – ab + b²)", Factorise x^2 + x^5​

Answer 1

Step-by-step solution:

$x^{2}+x^{5}=x^{2} (1+x^{3})$

            $=x^{2} (1^{3}+x^{3})$     -----------------------(1)

Here, a = 1 and b = x

Substituting in the given formula :-

=> $1^{3}+x^{3}= (1+x)(1-1*x+x)$    ------------------(2)

Now, put (2) in (1); we get

$x^{2}+ x^{5} = x^{2}(1+x)(x^{2}-x+1)$