Question

Factorize: (x + 2) (x² + 25 ) – 10x² – 20x.

Answer 1

(x + 2) (x² + 25) – 10x (x + 2) 

Take (x + 2 ) as common factor;

= (x + 2)(x² + 25 – 10x) 

= (x + 2) (x² – 10x + 25) 

Expanding the middle term of (x² – 10x + 25 ) 

= (x + 2) (x² – 5x – 5x + 25)

= (x + 2){x(x – 5) – 5( x – 5)} 

= (x + 2)(x – 5)(x – 5) 

= (x + 2)(x – 5)² 

Therefore, (x + 2) (x² + 25) – 10x(x + 2) = (x + 2)(x – 5)².