Question

factorise (x+2)³+(x-2)³

Answer 1

(x+2+x-2)(x+2^2 - (x+2)(x-2) + x-2^2 )

= 

2x(x^2 +2x +4 -x^2 +4 +x^2 -2x +4)

= 2x(x^2 +12)

Answer 2

On factoring (x+2)³+(x-2)³ we will get 2x and (x² + 12)  

Given:

Factorise (x+2)³+(x-2)³

To find:

Factors of (x+2)³+(x-2)³  

Solution:

From algebraic identities

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

Here given,

(x+2)³ + (x-2)³  

Take a = x and b = 2

Apply the above formula

=> (x+2)³ = x³ + 3x²2 + 3x2² + 2³  

=> (x+2)³ = x³ + 6x² + 12x + 8    

=> (x-2)³ = x³ - 3x²2 + 3x2² - 2³  

=> (x-2)³ = x³ - 6x² + 12x - 8    

From the above calculations,

(x+2)³+(x-2)³ = x³ + 6x² + 12x + 8 + x³ - 6x² + 12x - 8    

= x³ + 12x + x³ + 12x    

= 2x³ + 24x

= 2x [ x² + 12]  

Therefore,

On factoring (x+2)³+(x-2)³ we will get 2x and (x² + 12)  

     

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