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

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

Answer»

(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.

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