Question

factorize (a+b)3 - a - b

step by step plz
fast​

Answer 1

Required Answer:-

Given to Factorise:

• $\sf {(a + b)}^{3} - a - b$

Solution:

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

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

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

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

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

Hence, the factorised form is (a + b)(a + b + 1)(a + b - 1)

Identity Used:

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

Other Identities:

1. $\sf {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$
2. $\sf {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$
3. $\sf {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)$
4. $\sf {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)$
5. $\sf {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )$
6. $\sf {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )$

Answer 2

Answer:

(a+b)2

Step-by-step explanation:

$(a+b)3 - a - b$

Multiplying 3 with (a+b):

$=3a +3b - a - b$

$= 2a + 2b$

Taking 2 common from a and b:

$=(a+b)2\\ answer$