Question

factorize : (a +b)³ -a-b ​

Answer 1

Answer:

The given expression can be factorized as ( a + b ) ( a +b - 1 ) ( a + b + 1 )

Steps:

To Find:

Factorize the given equation.

Rewrite the given equation as,

= (a + b)^3 - a - b

= ( a + b )^3 - ( a + b )

( a + b ) [ ( a + b)^2 - 1^2 ]

Substitute the formula a^2 - b^2= ( a - b ) ( a + b )

in the above equation

= ( a + b ) ( a + b - 1 ) ( a + b + 1 )

Answer 2

Given,

$(a+b)^{3}-a-b$

We have find the factorize the given expression

Now,

$(a+b)^{3}-a-b$

$=$$=(a+b)^{3}-1(a+b)$

$= (a+b)((a+b)^{2}-1 )$

$=(a+b)((a+b)^{2}-1)$

Here, we have to using identity is

$x^{2} -y^{2}=(x-y)(x+y)$

Now, apply this identity, we get

$=(a+b)(a+b-1)(a+b+1)$

Therefore, the answer is$(a+b)(a+b-1)(a+b+1)$.