Question

(a+b)^3 - a - b pls factorise

Answer 1

Answer:

Sol : ( a + b )³ - a - b

= ( a + b )³ - ( a + b )

By taking ( a + b ) as common,

= ( a + b ) { ( a + b )² - 1 }

= ( a + b ) ( a² + b² + 2 ab - 1 ) [ ( a + b )² = a² + b² + 2 ab ]

Answer 2

ANSWER:

• Factorisation of the above expression is (a+b)(a+b+1)(a+b-1)

GIVEN:

• (a+b)³-a-b

TO FIND:

• Factorisation of the above expression.

SOLUTION:

= (a+b)³-(a+b)

= (a+b)[(a+b)²-1]

= (a+b)[(a+b)²-(1)²]

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

Factorisation of the above expression is (a+b)(a+b+1)(a+b-1)

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab