Factorize:(a + b)3 – (a – b)3

We know that,a3 - b3 = (a - b) (a2 + a × b + b2)Using this formula, we get= [a + b – (a – b)] [(a + b)2 + (a + b) (a – b) + (a – b)2]= (a + b – a + b) [a2 + b2 + 2ab + a2 – b2 + a2 + b2 – 2ab]= 2b (3a2 + b2)

Q. 213.5( 4 Votes )

Factorize:

(a + b)³ – (a – b)³

Class 9th RS Aggarwal & V Aggarwal - Mathematics 2. Polynomials

Answer :

We know that,

a³ - b³ = (a - b) (a² + a × b + b²)

Using this formula, we get

= [a + b – (a – b)] [(a + b)² + (a + b) (a – b) + (a – b)²]

= (a + b – a + b) [a² + b² + 2ab + a² – b² + a² + b² – 2ab]

= 2b (3a² + b²)

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